RSI Wave Function Ultimate OscillatorEnglish Explanation of the "RSI Wave Function Ultimate Oscillator" Pine Script Code
Understanding the Code
Purpose:
This Pine Script code creates a custom indicator that combines the Relative Strength Index (RSI) with a wave function to potentially provide more nuanced insights into market dynamics.
Key Components:
* Wave Function: This is a custom calculation that introduces a sinusoidal wave component to the price data. The frequency parameter controls the speed of the oscillation, and the decay factor determines how quickly the influence of past prices diminishes.
* Smoothed Signal: The wave function is applied to the closing price to create a smoothed signal, which is essentially a price series modulated by a sine wave.
* RSI: The traditional RSI is then calculated on this smoothed signal, providing a measure of the speed and change of price movements relative to recent price changes.
Calculation Steps:
* Wave Function Calculation:
* A sinusoidal wave is generated based on the bar index and the frequency parameter.
* The wave is combined with the closing price using a weighted average, where the decay factor determines the weight given to previous values.
* RSI Calculation:
* The RSI is calculated on the smoothed signal using a standard RSI formula.
* Plotting:
* The RSI values are plotted on a chart, along with horizontal lines at 70 and 30 to indicate overbought and oversold conditions.
* The area between the RSI line and the overbought/oversold lines is filled with color to visually represent the market condition.
Interpretation and Usage
* Wave Function: The wave function introduces cyclical patterns into the price data, which can help identify potential turning points or momentum shifts.
* RSI: The RSI provides a measure of the speed and change of price movements relative to recent price changes. When applied to the smoothed signal, it can help identify overbought and oversold conditions, as well as potential divergences between price and momentum.
* Combined Indicator: The combination of the wave function and RSI aims to provide a more sensitive and potentially earlier indication of market reversals.
* Signals:
* Crossovers: Crossovers of the RSI line above or below the overbought/oversold lines can be used to generate buy or sell signals.
* Divergences: Divergences between the price and the RSI can indicate a weakening trend.
* Oscillations: The amplitude and frequency of the oscillations in the RSI can provide insights into the strength and duration of market trends.
How it Reflects Market Volatility
* Amplified Volatility: The wave function can amplify the volatility of the price data, making it easier to identify potential turning points.
* Smoothing: The decay factor helps to smooth out short-term fluctuations, allowing the indicator to focus on longer-term trends.
* Sensitivity: The combination of the wave function and RSI can make the indicator more sensitive to changes in market momentum.
In essence, this custom indicator attempts to enhance traditional RSI analysis by incorporating a cyclical component that can potentially provide earlier signals of market reversals.
Note: The effectiveness of this indicator will depend on various factors, including the specific market, time frame, and the chosen values for the frequency and decay parameters. It is recommended to conduct thorough backtesting and optimize the parameters to suit your specific trading strategy.
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CMF and Scaled EFI OverlayCMF and Scaled EFI Overlay Indicator
Overview
The CMF and Scaled EFI Overlay indicator combines the Chaikin Money Flow (CMF) and a scaled version of the Elder Force Index (EFI) into a single chart. This allows traders to analyze both indicators simultaneously, facilitating better insights into market momentum and volume dynamics , specifically focusing on buying/selling pressure and momentum , without compromising the integrity of either indicator.
Purpose
Chaikin Money Flow (CMF): Measures buying and selling pressure by evaluating price and volume over a specified period. It indicates accumulation (buying pressure) when values are positive and distribution (selling pressure) when values are negative.
Elder Force Index (EFI): Combines price changes and volume to assess the momentum behind market moves. Positive values indicate upward momentum (prices rising with strong volume), while negative values indicate downward momentum (prices falling with strong volume).
By scaling the EFI to match the amplitude of the CMF, this indicator enables a direct comparison between pressure and momentum , preserving their shapes and zero crossings. Traders can observe the relationship between price movements, volume, and momentum more effectively, aiding in decision-making.
Understanding Pressure vs. Momentum
Chaikin Money Flow (CMF):
- Indicates the level of demand (buying pressure) or supply (selling pressure) in the market based on volume and price movements.
- Accumulation: When institutional or large investors are buying significant amounts of an asset, leading to an increase in buying pressure.
- Distribution: When these investors are selling off their holdings, increasing selling pressure.
Elder Force Index (EFI):
- Measures the strength and speed of price movements, indicating how forceful the current trend is.
- Positive Momentum: Prices are rising quickly, indicating a strong uptrend.
- Negative Momentum: Prices are falling rapidly, indicating a strong downtrend.
Understanding the difference between pressure and momentum is crucial. For example, a market may exhibit strong buying pressure (positive CMF) but weak momentum (low EFI), suggesting accumulation without significant price movement yet.
Features
Overlay of CMF and Scaled EFI: Both indicators are plotted on the same chart for easy comparison of pressure and momentum dynamics.
Customizable Parameters: Adjust lengths for CMF and EFI calculations and fine-tune the scaling factor for optimal alignment.
Preserved Indicator Integrity: The scaling method preserves the shape and zero crossings of the EFI, ensuring accurate analysis.
How It Works
CMF Calculation:
- Calculates the Money Flow Multiplier (MFM) and Money Flow Volume (MFV) to assess buying and selling pressure.
- CMF is computed by summing the MFV over the specified length and dividing by the sum of volume over the same period:
CMF = (Sum of MFV over n periods) / (Sum of Volume over n periods)
EFI Calculation:
- Calculates the EFI using the Exponential Moving Average (EMA) of the price change multiplied by volume:
EFI = EMA(n, Change in Close * Volume)
Scaling the EFI:
- The EFI is scaled by multiplying it with a user-defined scaling factor to match the CMF's amplitude.
Plotting:
- Both the CMF and the scaled EFI are plotted on the same chart.
- A zero line is included for reference, aiding in identifying crossovers and divergences.
Indicator Settings
Inputs
CMF Length (`cmf_length`):
- Default: 20
- Description: The number of periods over which the CMF is calculated. A higher value smooths the indicator but may delay signals.
EFI Length (`efi_length`):
- Default: 13
- Description: The EMA length for the EFI calculation. Adjusting this value affects the sensitivity of the EFI to price changes.
EFI Scaling Factor (`efi_scaling_factor`):
- Default: 0.000001
- Description: A constant used to scale the EFI to match the CMF's amplitude. Fine-tuning this value ensures the indicators align visually.
How to Adjust the EFI Scaling Factor
Start with the Default Value:
- Begin with the default scaling factor of `0.000001`.
Visual Inspection:
- Observe the plotted indicators. If the EFI appears too large or small compared to the CMF, proceed to adjust the scaling factor.
Fine-Tune the Scaling Factor:
- Increase or decrease the scaling factor incrementally (e.g., `0.000005`, `0.00001`, `0.00005`) until the amplitudes of the CMF and EFI visually align.
- The optimal scaling factor may vary depending on the asset and timeframe.
Verify Alignment:
- Ensure that the scaled EFI preserves the shape and zero crossings of the original EFI.
- Overlay the original EFI (if desired) to confirm alignment.
How to Use the Indicator
Analyze Buying/Selling Pressure and Momentum:
- Positive CMF (>0): Indicates accumulation (buying pressure).
- Negative CMF (<0): Indicates distribution (selling pressure).
- Positive EFI: Indicates positive momentum (prices rising with strong volume).
- Negative EFI: Indicates negative momentum (prices falling with strong volume).
Look for Indicator Alignment:
- Both CMF and EFI Positive:
- Suggests strong bullish conditions with both buying pressure and upward momentum.
- Both CMF and EFI Negative:
- Indicates strong bearish conditions with selling pressure and downward momentum.
Identify Divergences:
- CMF Positive, EFI Negative:
- Buying pressure exists, but momentum is negative; potential for a bullish reversal if momentum shifts.
- CMF Negative, EFI Positive:
- Selling pressure exists despite rising prices; caution advised as it may indicate a potential bearish reversal.
Confirm Signals with Other Analysis:
- Use this indicator in conjunction with other technical analysis tools (e.g., trend lines, support/resistance levels) to confirm trading decisions.
Example Usage
Scenario 1: Bullish Alignment
- CMF Positive: Indicates accumulation (buying pressure).
- EFI Positive and Increasing: Shows strengthening upward momentum.
- Interpretation:
- Strong bullish signal suggesting that buyers are active, and the price is likely to continue rising.
- Action:
- Consider entering a long position or adding to existing ones.
Scenario 2: Bearish Divergence
- CMF Negative: Indicates distribution (selling pressure).
- EFI Positive but Decreasing: Momentum is positive but weakening.
- Interpretation:
- Potential bearish reversal; price may be rising but underlying selling pressure suggests caution.
- Action:
- Be cautious with long positions; consider tightening stop-losses or preparing for a possible trend reversal.
Tips
Adjust for Different Assets:
- The optimal scaling factor may differ across assets due to varying price and volume characteristics.
- Always adjust the scaling factor when analyzing a new asset.
Monitor Indicator Crossovers:
- Crossings above or below the zero line can signal potential trend changes.
Watch for Divergences:
- Divergences between the CMF and EFI can provide early warning signs of trend reversals.
Combine with Other Indicators:
- Enhance your analysis by combining this overlay with other indicators like moving averages, RSI, or Ichimoku Cloud.
Limitations
Scaling Factor Sensitivity:
- An incorrect scaling factor may misalign the indicators, leading to inaccurate interpretations.
- Regular adjustments may be necessary when switching between different assets or timeframes.
Not a Standalone Indicator:
- Should be used as part of a comprehensive trading strategy.
- Always consider other market factors and indicators before making trading decisions.
Disclaimer
No Guarantee of Performance:
- Past performance is not indicative of future results.
- Trading involves risk, and losses can exceed deposits.
Use at Your Own Risk:
- This indicator is provided for educational purposes.
- The author is not responsible for any financial losses incurred while using this indicator.
Code Summary
//@version=5
indicator(title="CMF and Scaled EFI Overlay", shorttitle="CMF & Scaled EFI", overlay=false)
cmf_length = input.int(20, minval=1, title="CMF Length")
efi_length = input.int(13, minval=1, title="EFI Length")
efi_scaling_factor = input.float(0.000001, title="EFI Scaling Factor", minval=0.0, step=0.000001)
// --- CMF Calculation ---
ad = high != low ? ((2 * close - low - high) / (high - low)) * volume : 0
mf = math.sum(ad, cmf_length) / math.sum(volume, cmf_length)
// --- EFI Calculation ---
efi_raw = ta.ema(ta.change(close) * volume, efi_length)
// --- Scale EFI ---
efi_scaled = efi_raw * efi_scaling_factor
// --- Plotting ---
plot(mf, color=color.green, title="CMF", linewidth=2)
plot(efi_scaled, color=color.red, title="EFI (Scaled)", linewidth=2)
hline(0, color=color.gray, title="Zero Line", linestyle=hline.style_dashed)
- Lines 4-6: Define input parameters for CMF length, EFI length, and EFI scaling factor.
- Lines 9-11: Calculate the CMF.
- Lines 14-16: Calculate the EFI.
- Line 19: Scale the EFI by the scaling factor.
- Lines 22-24: Plot the CMF, scaled EFI, and zero line.
Feedback and Support
Suggestions: If you have ideas for improvements or additional features, please share your feedback.
Support: For assistance or questions regarding this indicator, feel free to contact the author through TradingView.
---
By combining the CMF and scaled EFI into a single overlay, this indicator provides a powerful tool for traders to analyze market dynamics more comprehensively. Adjust the parameters to suit your trading style, and always practice sound risk management.
Pulse Oscillator [UAlgo]The "Pulse Oscillator " is a trading tool designed to capture market momentum and trend changes by combining the strengths of multiple well-known technical indicators. By integrating the RSI (Relative Strength Index), CCI (Commodity Channel Index), and Stochastic Oscillator, this indicator provides traders with a comprehensive view of market conditions, offering both trend filtering and precise buy/sell signals. The oscillator is customizable, allowing users to fine-tune its parameters to match different trading strategies and timeframes. With its built-in smoothing techniques and level adjustments, the Pulse Oscillator aims to be a reliable tool for both trend-following and counter-trend trading strategies.
🔶 Key Features
Multi-Indicator Integration: Combines RSI, CCI, and Stochastic Oscillator to create a weighted momentum oscillator.
Why Use Multi-Indicator Integration?
Script uses Multi-Indicator Integration to combine the strengths of different technical indicators—such as RSI, CCI, and Stochastic Oscillator—into a single tool. This approach helps to reduce the weaknesses of individual indicators, providing a more comprehensive and reliable analysis of market conditions. By integrating multiple indicators, we can generate more accurate signals, filter out noise, and enhance our trading decisions.
Customizable Parameters: Allows users to adjust weights, periods, and smoothing techniques, providing flexibility to adapt the indicator to various market conditions.
Trend Filtering Option: An optional trend filter is available to enhance the accuracy of buy and sell signals, reducing the risk of false signals in choppy markets.
Dynamic Levels: The indicator dynamically calculates multiple levels of support and resistance, adjusting to market conditions with customizable decay factors and offsets.
Visual Clarity: The indicator visually represents different levels and trends with color-coded plots and fills, making it easier for traders to interpret market conditions at a glance.
Alerts: Configurable alerts for buy and sell signals, as well as trend changes, enabling traders to stay informed of key market movements without constant monitoring.
🔶 Interpreting the Indicator
Buy Signal: A buy signal is generated when the Slow Line crosses under the Fast Line during an uptrend or when the trend filter is disabled. This indicates a potential bullish reversal or continuation of an upward trend.
Sell Signal: A sell signal occurs when the Slow Line crosses above the Fast Line during a downtrend or when the trend filter is disabled, signaling a potential bearish reversal or continuation of a downward trend.
Trend Change: The indicator detects trend changes when the Fast Line shifts from increasing to decreasing or vice versa, providing early warning of possible market reversals.
Dynamic Levels: The indicator calculates upper and lower levels based on the Fast Line's values. These levels can be used to identify overbought or oversold conditions and potential areas of support or resistance.
🔶 Disclaimer
Use with Caution: This indicator is provided for educational and informational purposes only and should not be considered as financial advice. Users should exercise caution and perform their own analysis before making trading decisions based on the indicator's signals.
Not Financial Advice: The information provided by this indicator does not constitute financial advice, and the creator (UAlgo) shall not be held responsible for any trading losses incurred as a result of using this indicator.
Backtesting Recommended: Traders are encouraged to backtest the indicator thoroughly on historical data before using it in live trading to assess its performance and suitability for their trading strategies.
Risk Management: Trading involves inherent risks, and users should implement proper risk management strategies, including but not limited to stop-loss orders and position sizing, to mitigate potential losses.
No Guarantees: The accuracy and reliability of the indicator's signals cannot be guaranteed, as they are based on historical price data and past performance may not be indicative of future results.
Saral Relative StrengthRelative Strength Indicator
### Overview
The Relative Strength (RS) Indicator is a robust tool designed to measure the performance of a security relative to a benchmark or another security. Unlike traditional indicators, this RS Indicator calculates the outperformance or underperformance in percentage terms, providing a clear and concise comparison.
The equation for calculation can be found in the code itself. This equation compares how much a security's price has changed over a given period (len) relative to the change in price of a benchmark over the same period. The result is expressed as a percentage, showing whether the security has outperformed or underperformed the benchmark. A positive RS value indicates outperformance, while a negative value signals underperformance.
Basically, this indicator is an enhanced version of 'Relative Strength' indicator of 'BharatTrader' Sir with added features like automatic divergence plotting, color-coded filled area and sector names for NSE F&O securities. Default values for some of the parameters are based on discussion by Subhadip Nandy Sir in Trader's Talk with Mr. Rohit Katwal.
### Input Parameters:
Source: The price of a security used in the calculation, with the default being the 'close' price.
Comparative Symbol: Ticker ID of the comparative security, with the default set to NIFTY 50.
Period-RS: The period for calculating the RS line, with a default of 22. The RS line measures the relative performance of the security against the benchmark, helping to identify outperformance or underperformance over time.
Period-MA: The period for calculating the Simple Moving Average (SMA) overlay on the RS line, with a default of 11. The SMA provides a smoothed view of the RS line, helping to identify trends more clearly.
Lookback - Zero Line Trend: Zero Line Trend look-back period, used to determine the angle of the RS line, with a default of 5. This parameter influences the color of the Zero Line based on whether the RS line’s angle is positive or negative.
Lookback - Divergence: Divergence look-back period, with a default of 2, used to detect divergence between the price and the RS line.
Display MA Line: Controls the display of the SMA line. When enabled, the SMA line is plotted over the RS line to indicate trend strength.
Toggle RS Color on MA Crossovers: Controls the color of the RS line. If disabled, the RS line is purple. If enabled, the RS line changes color based on its position relative to the SMA: green for RS > MA, red for RS < MA.
Display Zero Line Trend: Controls the display of the Zero Line. If disabled, the Zero Line is black. If enabled, the Zero Line’s color changes to green or maroon based on the RS line’s angle over time.
Display Divergence: Controls the display of divergence dots on the RS line, indicating potential reversal points.
Display Filled Area: Controls whether the area between the Zero Line and the RS line is filled with color. The fill color changes based on the relationship of the RS line with the SMA & Zero Line as given below.
- Dark Green: RS > 0 and RS > MA, indicating strong outperformance.
- Light Green: RS > 0 and RS < MA, indicating weakening outperformance.
- Dark Red: RS < 0 and RS < MA, indicating strong underperformance.
- Light Red: RS < 0 and RS > MA, indicating weakening underperformance.
Display Sector Name: Controls the display of sector names for NSE F&O securities, helping to plot RS with sectoral indices.
### Key Features:
RS Line:
The RS line represents the relative performance of a security against a benchmark over a specified period (default 22). It helps traders identify whether the security is outperforming or underperforming the benchmark.
SMA Overlay:
A Simple Moving Average (SMA) line is plotted over the RS line, with a default period of 11. The SMA provides a smoothed trend of the RS, making it easier to identify consistent performance trends.
Trend-Sensitive Zero Line:
The Zero Line’s color adapts based on the RS line’s trend:
- Green: Positive angle of the RS line, indicating upward momentum.
- Maroon: Negative angle, indicating downward momentum.
The color can be toggled, with an option to display the Zero Line in black.
Divergence Detection:
Automatically detects and highlights divergences.
- Positive Divergence: RS line rises while the price falls, marked by blue dots.
- Negative Divergence: RS line falls while the price rises, marked by black dots.
Color-Coded Fill Area:
The area between the RS line and the Zero Line is filled with color to visually distinguish different market conditions, with Dark and Light colors providing insight into the strength of the performance:
- Dark Green: Indicates strong outperformance (RS > 0 and RS > MA), suggesting the security is showing significant strength compared to the benchmark.
- Light Green: Indicates weakening outperformance (RS > 0 and RS < MA), signaling that while the security is still outperforming, its strength is diminishing.
- Dark Red: Indicates strong underperformance (RS < 0 and RS < MA), showing the security is significantly weaker than the benchmark.
- Light Red: Indicates weakening underperformance (RS < 0 and RS > MA), suggesting the security is still underperforming but may be regaining some strength.
Sectoral Strength:
Displays sector names for NSE F&O securities, helping users to compare the RS of individual securities with their respective sectoral indices. Comparative Security can be changed easily based on this sector name. Users need not to remember sector names for individual securities.
If any security is not categorized in a specific sector, CNX500 has been considered as a default sector for NSE F&O securities. For other securities, NIFTY50 has been considered as a default sector.
S&P 2024: Magnificent 7 vs. the rest of S&PThis chart is designed to calculate and display the percentage change of the Magnificent 7 (M7) stocks and the S&P 500 excluding the M7 (Ex-M7) from the beginning of 2024 to the most recent data point. The Magnificent 7 consists of seven major technology stocks: Apple (AAPL), Microsoft (MSFT), Amazon (AMZN), Alphabet (GOOGL), Meta (META), Nvidia (NVDA), and Tesla (TSLA). These stocks are a significant part of the S&P 500 and can have a substantial impact on its overall performance.
Key Components and Functionality:
1. Start of 2024 Baseline:
- The script identifies the closing prices of the S&P 500 and each of the Magnificent 7 stocks on the first trading day of 2024. These values serve as the baseline for calculating percentage changes.
2. Current Value Calculation:
- It then fetches the most recent closing prices of these stocks and the S&P 500 index to calculate their current values.
3. Percentage Change Calculation:
- The script calculates the percentage change for the M7 by comparing the sum of the current prices of the M7 stocks to their combined value at the start of 2024.
- Similarly, it calculates the percentage change for the Ex-M7 by comparing the current value of the S&P 500 excluding the M7 to its value at the start of 2024.
4. Plotting:
- The calculated percentage changes are plotted on the chart, with the M7’s percentage change shown in red and the Ex-M7’s percentage change shown in blue.
Use Case:
This indicator is particularly useful for investors and analysts who want to understand how much the performance of the S&P 500 in 2024 is driven by the Magnificent 7 stocks compared to the rest of the index. By showing the percentage change from the start of the year, it provides clear insights into the relative growth or decline of these two segments of the market over the course of the year.
Visualization:
- Red Line (M7 % Change): Displays the percentage change of the combined value of the Magnificent 7 stocks since the start of 2024.
- Blue Line (Ex-M7 % Change): Displays the percentage change of the S&P 500 excluding the Magnificent 7 since the start of 2024.
This script enables a straightforward comparison of the performance of the M7 and Ex-M7, highlighting which segment is contributing more to the overall movement of the S&P 500 in 2024.
Follow the Volumes / Path of Least ResistanceThis indicator tracks price movements following significant volume increases. It identifies volume spikes by comparing recent average volume to a longer-term average. After a spike, it monitors price changes over a specified number of bars.
In plain English, the point of this is to “let the market show it’s hand”, vs. other common and preemptive methods of execution.
You can think of it as a better version of a volume up/down indicator which only uses opening and closing prices to identify "bullish" or "bearish" behavior.
To optimize this, I used a very small range chart, hence the small values. You will need to experiment with other values, ESPECIALLY the % change. If you do not do this, the indicator will generate a lot of noise.
The indicator has three main conditions:
1. Significant price increase, bullish: A green triangle appears below the bar.
2. Significant price decrease, bearish: A red triangle appears above the bar.
3. Price change within thresholds: A fuschia triangle appears, pointing up or down based on the overall (short-term) trend. This is common behavior during trends. A spike in volume will appear, and price simply does not budge. Volume/price is essentially declaring a new found value, in which case prices tend to follow the impulse movement (see market profile theory).
The color scheme is intuitive: green for positive moves, red for negative, and fuschia for subtle changes following the existing trend. Blue circles mark volume spikes for reference, which I recommend using only for reference, and disabling to remove unneeded noise.
Because this indicator "lags" in the sense of waiting for the market to show its hand, best opportunities are typically found on retests of the volume spikes themselves. On drives, however, the market will unlikely pullback, which (in my view) is one of its best use cases.
Bottom line, you will need to adjust the parameters to the instrument. This is not a plug and play solution, but far more accurate than those which are.
Settings, and what they mean:
Volume spike average bars: length for identification of high volumes. On smaller timeframes, such as my optimization period, you’ll want several bars. But on something such as a 5 minute or higher, only 1.
Lookback period: for identification of high volumes.
Volume Increase Threshold (%): % which constitutes a jump in volume
Bars After Spike: How long to wait for ensuing price movement. Also sensitive to the timeframe you are using. 1-2 recommended for 5m+, more for smaller range-based.
Negative Price Change Threshold (%): For red arrows (Volume + Price Movement)
Positive Price Change Threshold (%): Inverse of above
WMA Period for Stability Function: When price spikes on high volumes but does not move (price is “trapped” between negative and positive price change thresholds) the indicator marks direction (in fuchsia) in the direction of the underlying trend. This short-term MA identifies that trend.
Finally, because this indicator is volume-based, I recommend using primary instruments only and discourage its use on CFDs or other firm-generated instruments. Just use the primary. I would ignore signals off the open, which is subject to erroneous behavior. Other methods are far more effective for that.
This script is purposely uncomplicated. Feel free to play with settings and change code to suit your needs.
Sharpe and Sortino Ratios█ OVERVIEW
This indicator calculates the Sharpe and Sortino ratios using a chart symbol's periodic price returns, offering insights into the symbol's risk-adjusted performance. It features the option to calculate these ratios by comparing the periodic returns to a fixed annual rate of return or the returns from another selected symbol's context.
█ CONCEPTS
Returns, risk, and volatility
The return on an investment is the relative gain or loss over a period, often expressed as a percentage. Investment returns can originate from several sources, including capital gains, dividends, and interest income. Many investors seek the highest returns possible in the quest for profit. However, prudent investing and trading entails evaluating such returns against the associated risks (i.e., the uncertainty of returns and the potential for financial losses) for a clearer perspective on overall performance and sustainability.
The profitability of an investment typically comes at the cost of enduring market swings, noise, and general uncertainty. To navigate these turbulent waters, investors and portfolio managers often utilize volatility , a measure of the statistical dispersion of historical returns, as a foundational element in their risk assessments because it provides a tangible way to gauge the uncertainty in returns. High volatility suggests increased uncertainty and, consequently, higher risk, whereas low volatility suggests more stable returns with minimal fluctuations, implying lower risk. These concepts are integral components in several risk-adjusted performance metrics, including the Sharpe and Sortino ratios calculated by this indicator.
Risk-free rate
The risk-free rate represents the rate of return on a hypothetical investment carrying no risk of financial loss. This theoretical rate provides a benchmark for comparing the returns on a risky investment and evaluating whether its excess returns justify the risks. If an investment's returns are at or below the theoretical risk-free rate or the risk premium is below a desired amount, it may suggest that the returns do not compensate for the extra risk, which might be a call to reassess the investment.
Since the risk-free rate is a theoretical concept, investors often utilize proxies for the rate in practice, such as Treasury bills and other government bonds. Conventionally, analysts consider such instruments "risk-free" for a domestic holder, as they are a form of government obligation with a low perceived likelihood of default.
The average yield on short-term Treasury bills, influenced by economic conditions, monetary policies, and inflation expectations, has historically hovered around 2-3% over the long term. This range also aligns with central banks' inflation targets. As such, one may interpret a value within this range as a minimum proxy for the risk-free rate, as it may correspond to the minimum rate required to maintain purchasing power over time. This indicator uses a default value of 2% as the risk-free rate in its Sharpe and Sortino ratio calculations. Users can adjust this value from the "Risk-free rate of return" input in the "Settings/Inputs" tab.
Sharpe and Sortino ratios
The Sharpe and Sortino ratios are two of the most widely used metrics that offer insight into an investment's risk-adjusted performance . They provide a standardized framework to compare the effectiveness of investments relative to their perceived risks. These metrics can help investors determine whether the returns justify the risks taken to achieve them, promoting more informed investment decisions.
Both metrics measure risk-adjusted performance similarly. However, they have some differences in their formulas and their interpretation:
1. Sharpe ratio
The Sharpe ratio , developed by Nobel laureate William F. Sharpe, measures the performance of an investment compared to a theoretically risk-free asset, adjusted for the investment risk. The ratio uses the following formula:
Sharpe Ratio = (𝑅𝑎 − 𝑅𝑓) / 𝜎𝑎
Where:
• 𝑅𝑎 = Average return of the investment
• 𝑅𝑓 = Theoretical risk-free rate of return
• 𝜎𝑎 = Standard deviation of the investment's returns (volatility)
A higher Sharpe ratio indicates a more favorable risk-adjusted return, as it signifies that the investment produced higher excess returns per unit of increase in total perceived risk.
2. Sortino ratio
The Sortino ratio is a modified form of the Sharpe ratio that only considers downside volatility , i.e., the volatility of returns below the theoretical risk-free benchmark. Although it shares close similarities with the Sharpe ratio, it can produce very different values, especially when the returns do not have a symmetrical distribution, since it does not penalize upside and downside volatility equally. The ratio uses the following formula:
Sortino Ratio = (𝑅𝑎 − 𝑅𝑓) / 𝜎𝑑
Where:
• 𝑅𝑎 = Average return of the investment
• 𝑅𝑓 = Theoretical risk-free rate of return
• 𝜎𝑑 = Downside deviation (standard deviation of negative excess returns, or downside volatility)
The Sortino ratio offers an alternative perspective on an investment's return-generating efficiency since it does not consider upside volatility in its calculation. A higher Sortino ratio signifies that the investment produced higher excess returns per unit of increase in perceived downside risk.
The risk-free rate (𝑅𝑓) in the numerator of both ratio formulas acts as a baseline for comparing an investment's performance to a theoretical risk-free alternative. By subtracting the risk-free rate from the expected return (𝑅𝑎−𝑅𝑓), the numerator essentially represents the risk premium of the investment.
Comparison with another symbol
In addition to the conventional Sharpe and Sortino ratios, which compare an instrument's returns to a risk-free rate, this indicator can also compare returns to a user-specified benchmark symbol , allowing the calculation of Information ratios .
An Information ratio is a generalized form of the Sharpe ratio that compares an investment's returns to a risky benchmark , such as SPY, rather than a risk-free rate. It measures the investment's active return (the difference between its returns and the benchmark returns) relative to its tracking error (i.e., the volatility of the active return) using the following formula:
𝐼𝑅 = (𝑅𝑝 − 𝑅𝑏) / 𝑇𝐸
Where:
• 𝑅𝑝 = Average return on the portfolio or investment
• 𝑅𝑏 = Average return from the benchmark instrument
• 𝑇𝐸 = Tracking error (volatility of 𝑅𝑝 − 𝑅𝑏)
Comparing returns to a benchmark instrument rather than a theoretical risk-free rate offers unique insights into risk-adjusted performance. Higher Information ratios signify that the investment produced higher active returns per unit of increase in risk relative to the benchmark. Conventional choices for non-risk-free benchmarks include major composite indices like the S&P 500 and DJIA, as the resulting ratios can provide insight into the effectiveness of an investment relative to the broader market.
Users can enable this generalized calculation for both the Sharpe and Sortino ratios by selecting the "Benchmark symbol returns" option from the "Benchmark type" dropdown in the "Settings/Inputs" tab.
It's crucial to note that this indicator compares the charts symbol's rate of change (return) to the rate of change in the benchmark symbol. Consequently, not all symbols available on TradingView are suitable for use with these ratios due to the nature of what their values represent. For instance, using a bond as a benchmark will produce distorted results since each bar's values represent yields rather than prices, meaning it compares the rate of change in the yield. To maintain consistency and relevance in the calculated ratios, ensure the values from the compared symbols strictly represent price information.
█ FEATURES
This indicator provides traders with two widely used metrics for assessing risk-adjusted performance, generalized to allow users to compare the chart symbol's price returns to a fixed risk-free rate or the returns from another risky symbol. Below are the key features of this indicator:
Timeframe selection
The "Returns timeframe" input determines the timeframe of the calculated price returns. Users can select any value greater than or equal to the chart's timeframe. The default timeframe is "1M".
Periodic returns tracking
This indicator compounds and collects requested price returns from the selected timeframe over monthly or daily periods, similar to how the Broker Emulator works when calculating strategy performance metrics on trade data. It employs the following logic:
• Track returns over monthly periods if the chart's data spans at least two months.
• Track returns over daily periods if the chart's data spans at least two days but not two months.
• Do not track or collect returns if the data spans less than two days, as the amount of data is insufficient for meaningful ratio calculations.
The indicator uses the returns collected from up to a specified number of periods to calculate the Sharpe and Sortino ratios, depending on the available historical data. It also uses these periodic returns to calculate the average returns it displays in the Data Window.
Users can control the maximum number of periods the indicator analyzes with the "Max no. of periods used" input in the "Settings/Inputs" tab. The default value is 60 periods.
Benchmark specification
The "Benchmark return type" input specifies the benchmark type the indicator compares to the chart symbol's returns in the ratio calculations. It features the following two options:
• "Risk-free rate of return (%)": Compares the price returns to a user-specified annual rate of return representing a theoretical risk-free rate (e.g., 2%).
• "Benchmark symbol return": Compares the price returns to a selected benchmark symbol (e.g., "AMEX:SPY) to calculate Information ratios.
When comparing a chart symbol's returns to a specified benchmark symbol, this indicator aligns the times of data points from the benchmark with the times of data points from the chart's symbol to facilitate a fair comparison between symbols with different active sessions.
Visualization and display
• The indicator displays the periodic returns requested from the specified "Returns timeframe" in a separate pane. The plot includes dynamic colors to signify positive and negative returns.
• When the "Returns timeframe" value represents a higher timeframe, the indicator displays background highlights on the main chart pane to signify when a new value is available and whether the return is positive or negative.
• When the specified benchmark return type is a benchmark symbol, the indicator displays the requested symbol's returns in the separate pane as a gray line for visual comparison.
• Within the separate pane, the indicator displays a single-cell table that shows the base period it uses for periodic returns, the number of periods it uses in the calculation, the timeframe of the requested data, and the calculated Sharpe and Sortino ratios.
• The Data Window displays the chart symbol and benchmark returns, their periodic averages, and the Sharpe and Sortino ratios.
█ FOR Pine Script™ CODERS
• This script utilizes the functions from our RiskMetrics library to determine the size of the periods, calculate and collect periodic returns, and compute the Sharpe and Sortino ratios.
• The `getAlignedPrices()` function in this script requests price data for the chart's symbol and a benchmark symbol with consistent time alignment by utilizing spread symbols , which helps facilitate a fair comparison between different symbol types. Retrieving prices from spreads avoids potential information loss and data misalignment that can otherwise occur when using separate requests from each symbol's context when those symbols have different sessions or data times.
• For consistency, the `getAlignedPrices()` function includes extended hours and dividend adjustment modifiers in its data requests. Additionally, it includes other settings inherited from the chart's context, such as "settlement-as-close" preferences for fair comparison between futures instruments.
• This script uses the `changePercent()` function from our ta library to calculate the percentage changes of the requested data.
• The newly released `force_overlay` parameter in display-related functions allows indicators to display visuals on the main chart and a separate pane simultaneously. We use the parameter in this script's bgcolor() call to display background highlights on the main chart.
Look first. Then leap.
Consolidation Channels (AstroHub)Consolidation Channels (AstroHub) Indicator
Overview:
The Consolidation Channels (AstroHub) indicator is a powerful tool designed for traders seeking to identify consolidation periods within financial markets. Unlike traditional indicators that merely follow trends or focus on specific trading strategies, this script utilizes a unique approach based on fractal dimension calculations and multidimensional momentum analysis to detect consolidation zones in price action.
Key Concepts:
Fractal Dimension (Di):
The script employs the concept of fractal dimension to define the consolidation period (N). The user can customize this parameter to adjust the sensitivity of the indicator to consolidation patterns.
Multidimensional Momentum (M):
Multidimensional momentum is calculated by assessing the interaction between the closing prices (Pi) and opening prices (Pj) over a specified period (T). This dynamic calculation provides a comprehensive view of momentum changes in the market.
Consolidation Start:
The indicator marks the beginning of consolidation by identifying the lowest point in the multidimensional momentum. The consolidation start line is displayed on the chart, providing a clear reference for traders.
High and Low Lines:
High and low lines are drawn from the highest and lowest price levels over the consolidation period. These lines help visualize the upper and lower bounds of the consolidation channel.
Bar Color Change:
The color of each bar changes based on whether the closing price is above or below the consolidation start line. This visual cue assists traders in quickly identifying shifts in market dynamics.
Dashed Lines into the Future:
Dashed lines extending into the future from the high and low points of consolidation provide a forward-looking perspective, aiding traders in anticipating potential price movements.
How to Use:
Customization:
Adjust the input parameters (N, r, T, Z, Color1, Color2, Color3) to suit your trading preferences and market conditions.
Interpretation:
Look for periods where the bar color changes, indicating shifts in market sentiment during consolidation. Pay attention to the start of consolidation, high, and low lines for potential reversal or breakout signals.
Alerts:
Set up alerts for key events such as reaching the lowest point, closing above the high line, or closing below the low line to stay informed about potential trading opportunities.
Conclusion:
The Consolidation Channels (AstroHub) indicator goes beyond conventional trend-following techniques, offering traders a unique perspective on market consolidation. By combining fractal dimension analysis and multidimensional momentum calculations, this script equips traders with a valuable tool for identifying potential reversal zones and making informed trading decisions.
Dope DPOThe "Dope DPO" (DDPO) indicator is a technical analysis tool designed for traders to identify trends and potential trend changes in the market. It's based on the concept of the Detrended Price Oscillator (DPO), but with several enhancements for greater versatility and user customization.
Key Features of the Dope DPO Indicator:
Averaging Multiple Periods: The indicator averages the DPO calculations over ten different time periods. This averaging helps in smoothing out the volatility and providing a more comprehensive view of the market trend.
Customizable Smoothing: Users can choose the length of the smoothing as well as the type of moving average (SMA, EMA, WMA, or RMA) for smoothing. This allows for flexibility in how the indicator responds to price changes.
Trend Change Detection: The indicator includes a feature to detect changes in the market trend. It does this by comparing the current value of the smoothed DPO to its value a specified number of bars back. This helps in identifying potential reversals or shifts in momentum.
Dynamic Color Coding: The indicator uses color coding (green and red) to visually represent the trend direction. If the smoothed DPO is trending upwards compared to a previous value, the color will be green, indicating bullish momentum. Conversely, a red color signifies bearish momentum.
Horizontal Reference Lines: It includes horizontal lines at specific levels (overbought, zero, and oversold) to provide reference points for interpreting the indicator's values.
Usage:
Traders can use the Dope DPO to gauge the overall market trend and to look for potential entry and exit points based on trend changes.
The color-coded histogram makes it easy to spot when the trend might be reversing, which can be particularly useful in conjunction with other technical analysis tools.
The flexibility in choosing the smoothing method and length allows traders to tailor the indicator to different trading styles and timeframes.
[MAD] Harmonic Wave Fourier AnalysisThis script uses Fourier Analysis with additional postcalculations to draw a plot which displays the Amplitude-Change of the Fouriers
Parameter Settings:
You can set the number of data points to analyze
the period to check for extremes.
Fourier Transform: The script breaks down the time series data into its frequency components using cosine and sine calculations.
Harmonic Analysis: It calculates the strength and phase of each frequency component, producing harmonic waves.
Amplitude Change: It determines the change in amplitude between peaks and troughs for each harmonic.
Latest Value Extraction: The script selects the middle amplitude change as the latest data point.
High/Low Points: Finds the maximum and minimum amplitude changes over a specified period.
Visualization: It plots the latest amplitude change with a color that indicates its value relative to the identified extremes.
splitted by 3 Blue plots (1/3 1/2 2/3 from min to max)
How to trade?
May go for retests to the blue lines after big moves.
See this script as braindump of an idea, so its just a concept :-)
Trend_Trader_WMA (Momentum)<---> Caution! This is first test version of indicator. I am ready to get more ideas+feedback to develop it more. <--->
The "Momentum_Trader_WMA" indicator is a versatile technical analysis tool designed to help traders identify potential trend changes and momentum shifts in the market. It combines multiple indicators and moving averages to provide a comprehensive view of price action and momentum.
Key Features:
Weighted Moving Averages (WMAs): The indicator calculates two different WMAs with user-defined lengths, providing a smoothed representation of price data.
Average True Range (ATR) Bands: ATR is used to calculate dynamic bands around the WMA Average. These bands can help traders gauge market volatility and potential breakout points. The color of the ATR bands can be seen as an early signal of trends or the continuation of current trends.
Commodity Channel Index (CCI): CCI is a momentum oscillator that measures the relative strength of price changes. The indicator calculates CCI values based on a user-defined period.
Exponential Moving Average (EMA) of CCI: An EMA of CCI is plotted to help identify trends and momentum shifts.
Color-Coded Bands: The ATR bands change colors based on CCI conditions, providing visual cues for potential trading opportunities. When ATR bands transition from narrow (indicating low volatility) to wide (indicating increased volatility), it can be seen as an early signal of a potential trend change or the continuation of the current trend.
Buy and Sell Signals: The indicator generates buy and sell signals based on crossovers of WMAs and CCI thresholds, making it easier for traders to identify entry and exit points.
Customizable Moving Averages: Traders can enable or disable different moving averages (e.g., SMA, EMA, WMA, RMA, VWMA, HMA) with various periods and colors to adapt the indicator to their trading preferences.
CCI Dot Alerts: Dots are displayed at the bottom of the chart based on CCI values, helping traders spot extreme CCI conditions.
How to Use:
Trend Identification: The WMAs and ATR bands can help identify the current trend direction and its strength. When the WMAs are in an uptrend (green) and the ATR bands widen, it may indicate a strong bullish trend. Conversely, when the WMAs are in a downtrend (red) and the ATR bands narrow, it may suggest a weakening bearish trend.
Momentum Confirmation: The CCI and its EMA provide insights into market momentum. Look for CCI crossovers above 100 for potential bullish momentum and below -100 for potential bearish momentum.
Buy and Sell Signals: Pay attention to the buy and sell signals generated by the indicator. Buy when the WMAs cross over and CCI crosses above 100. Sell when the WMAs cross under and CCI crosses below -100.
ATR Bands as Early Signals: The color changes in the ATR bands can be seen as early signals of trends or the continuation of current trends. Wide ATR bands may indicate increased volatility and potential trend changes, while narrow ATR bands suggest reduced volatility and potential trend continuation.
Moving Averages: Customize the indicator by enabling or disabling specific moving averages according to your preferred trading strategy.
CCI Dots: Use the CCI dots to identify extreme CCI conditions, which may indicate overbought or oversold market conditions.
PS:
Recommended to use Indicator with price action conecpts(eg. support and resistance) as they play important role in any market.
Buy and sell signals are not really accurate. I would personally look for trend shift in WMA middle line and confirmation from CCI dots at bottom. For example. If middle line turns green and within recent 3-4 candles (or next 3-4 candles) dots tunrns green also, that means momentum has been rised in the direction of bulls.
pls, take s/r concepts first when working. I am thinking to add more precise buy sell signal method to make it easier to trade.
Good luck with your trades :)
Advanced Volatility-Adjusted Momentum IndexAdvanced Volatility-Adjusted Momentum Index (AVAMI)
The AVAMI is a powerful and versatile trading index which enhances the traditional momentum readings by introducing a volatility adjustment. This results in a more nuanced interpretation of market momentum, considering not only the rate of price changes but also the inherent volatility of the asset.
Settings and Parameters:
Momentum Length: This parameter sets the number of periods used to calculate the momentum, which is essentially the rate of change of the asset's price. A shorter length value means the momentum calculation will be more sensitive to recent price changes. Conversely, a longer length will yield a smoother and more stabilized momentum value, thereby reducing the impact of short-term price fluctuations.
Volatility Length: This parameter is responsible for determining the number of periods to be considered in the calculation of standard deviation of returns, which acts as the volatility measure. A shorter length will result in a more reactive volatility measure, while a longer length will produce a more stable, but less sensitive measure of volatility.
Smoothing Length: This parameter sets the number of periods used to apply a moving average smoothing to the AVAMI and its signal line. The purpose of this is to minimize the impact of volatile periods and to make the indicator's lines smoother and easier to interpret.
Lookback Period for Scaling: This is the number of periods used when rescaling the AVAMI values. The rescaling process is necessary to ensure that the AVAMI values remain within a consistent and interpretable range over time.
Overbought and Oversold Levels: These levels are thresholds at which the asset is considered overbought (potentially overvalued) or oversold (potentially undervalued), respectively. For instance, if the AVAMI exceeds the overbought level, traders may consider it as a possible selling opportunity, anticipating a price correction. Conversely, if the AVAMI falls below the oversold level, it could be seen as a buying opportunity, with the expectation of a price bounce.
Mid Level: This level represents the middle ground between the overbought and oversold levels. Crossing the mid-level line from below can be perceived as an increasing bullish momentum, and vice versa.
Show Divergences and Hidden Divergences: These checkboxes give traders the option to display regular and hidden divergences between the AVAMI and the asset's price. Divergences are crucial market structures that often signal potential price reversals.
Index Logic:
The AVAMI index begins with the calculation of a simple rate of change momentum indicator. This raw momentum is then adjusted by the standard deviation of log returns, which acts as a measure of market volatility. This adjustment process ensures that the resulting momentum index encapsulates not only the speed of price changes but also the market's volatility context.
The raw AVAMI is then smoothed using a moving average, and a signal line is generated as an exponential moving average (EMA) of this smoothed AVAMI. This signal line serves as a trigger for potential trading signals when crossed by the AVAMI.
The script also includes an algorithm to identify 'fractals', which are distinct price patterns that often act as potential market reversal points. These fractals are utilized to spot both regular and hidden divergences between the asset's price and the AVAMI.
Application and Strategy Concepts:
The AVAMI is a versatile tool that can be integrated into various trading strategies. Traders can utilize the overbought and oversold levels to identify potential reversal points. The AVAMI crossing the mid-level line can signify a change in market momentum. Additionally, the identification of regular and hidden divergences can serve as potential trading signals:
Regular Divergence: This happens when the asset's price records a new high/low, but the AVAMI fails to follow suit, suggesting a possible trend reversal. For instance, if the asset's price forms a higher high but the AVAMI forms a lower high, it's a regular bearish divergence, indicating potential price downturn.
Hidden Divergence: This is observed when the price forms a lower high/higher low, but the AVAMI forms a higher high/lower low, suggesting the continuation of the prevailing trend. For example, if the price forms a lower low during a downtrend, but the AVAMI forms a higher low, it's a hidden bullish divergence, signaling the potential continuation of the downtrend.
As with any trading tool, the AVAMI should not be used in isolation but in conjunction with other technical analysis tools and within the context of a well-defined trading plan.
120x ticker screener (composite tickers)In specific circumstances, it is possible to extract data, far above the 40 `request.*()` call limit for 1 single script .
The following technique uses composite tickers . Changing tickers needs to be done in the code itself as will be explained further.
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
🔶 PRINCIPLE
Standard example:
c1 = request.security('MTLUSDT' , 'D', close)
This will give the close value from 1 ticker (MTLUSDT); c1 for example is 1.153
Now let's add 2 tickers to MTLUSDT; XMRUSDT and ORNUSDT with, for example, values of 1.153 (I), 143.4 (II) and 0.8242 (III) respectively.
Just adding them up 'MTLUSDT+XMRUSDT+ORNUSDT' would give 145.3772 as a result, which is not something we can use...
Let's multiply ORNUSDT by 100 -> 14340
and multiply MTLUSDT by 1000000000 -> 1153000000 (from now, 10e8 will be used instead of 1000000000)
Then we make the sum.
When we put this in a security call (just the close value) we get:
c1 = request.security('MTLUSDT*10e8+XMRUSDT*100+ORNUSDT', 'D', close)
'MTLUSDT*10e8+XMRUSDT*100+ORNUSDT' -> 1153000000 + 14340 + 0.8242 = 1153014340.8242 (a)
This (a) will be split later on, for example:
1153014330.8242 / 10e8 = 1.1530143408242 -> round -> in this case to 1.153 (I), multiply again by 10e8 -> 1153000000.00 (b)
We subtract this from the initial number:
1153014340.8242 (a)
- 1153000000.0000 (b)
–––––––––––––––––
14340.8242 (c)
Then -> 14340.8242 / 100 = 143.408242 -> round -> 143.4 (II) -> multiply -> 14340.0000 (d)
-> subtract
14340.8242 (c)
- 14340.0000 (d)
––––––––––––
0.8242 (III)
Now we have split the number again into 3 tickers: 1.153 (I), 143.4 (II) and 0.8242 (III)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
In this publication the function compose_3_() will make a composite ticker of 3 tickers, and the split_3_() function will split these 3 tickers again after passing 1 request.security() call.
In this example:
t46 = 'BINANCE:MTLUSDT', n46 = 10e8 , r46 = 3, t47 = 'BINANCE:XMRUSDT', n47 = 10e1, r47 = 1, t48 = 'BINANCE:ORNUSDT', r48 = 4 // T16
•••
T16= compose_3_(t48, t47, n47, t46, n46)
•••
= request.security(T16, res, )
•••
= split_3_(c16, n46, r46, n47, r47, r48)
🔶 CHANGING TICKERS
If you need to change tickers, you only have to change the first part of the script, USER DEFINED TICKERS
Back to our example, at line 26 in the code, you'll find:
t46 = 'BINANCE:MTLUSDT', n46 = 10e8 , r46 = 3, t47 = 'BINANCE:XMRUSDT', n47 = 10e1, r47 = 1, t48 = 'BINANCE:ORNUSDT', r48 = 4 // T16
( t46 , T16 ,... will be explained later)
You need to figure out how much you need to multiply each ticker, and the number for rounding, to get a good result.
In this case:
'BINANCE:MTLUSDT', multiply number = 10e8, round number is 3 (example value 1.153)
'BINANCE:XMRUSDT', multiply number = 10e1, round number is 1 (example value 143.4)
'BINANCE:ORNUSDT', NO multiply number, round number is 4 (example value 0.8242)
The value with most digits after the decimal point by preference is placed to the right side (ORNUSDT)
If you want to change these 3, how would you do so?
First pick your tickers and look for the round values, for example:
'MATICUSDT', example value = 0.5876 -> round -> 4
'LTCUSDT' , example value = 77.47 -> round -> 2
'ARBUSDT' , example value = 1.0231 -> round -> 4
Value with most digits after the decimal point -> MATIC or ARB, let's pick ARB to go on the right side, LTC at the left of ARB, and MATIC at the most left side.
-> 'MATICUSDT', LTCUSDT', ARBUSDT'
Then check with how much 'LTCUSDT' and 'MATICUSDT' needs to be multiplied to get this: 5876 0 7747 0 1.0231
'MATICUSDT' -> 10e10
'LTCUSDT' -> 10e3
Replace:
t46 = 'BINANCE:MTLUSDT', n46 = 10e8 , r46 = 3, t47 = 'BINANCE:XMRUSDT', n47 = 10e1, r47 = 1, t48 = 'BINANCE:ORNUSDT', r48 = 4 // T16
->
t46 = 'BINANCE:MATICUSDT', n46 = 10e10 , r46 = 4, t47 = 'BINANCE:LTCUSDT', n47 = 10e3, r47 = 2, t48 = 'BINANCE:ARBUSDT', r48 = 4 // T16
DO NOT change anything at t46, n46,... if you don't know what you're doing!
Only
• tickers ('BINANCE:MTLUSDT', 'BINANCE:XMRUSDT', 'BINANCE:ORNUSDT', ...),
• multiply numbers (10e8, 10e1, ...) and
• round numbers (3, 1, 4, ...)
should be changed.
There you go!
🔶 LIMITATIONS
🔹 The composite ticker fails when 1 of the 3 isn't in market in the weekend, while the other 2 are.
That is the reason all tickers are crypto. I think it is possible to combine stock,... tickers, but they have to share the same market hours.
🔹 The number cannot be as large as you want, the limit lays around 15-16 digits.
This means when you have for example 123, 45.67 and 0.000000000089, you'll get issues when composing to this:
-> 123045670.000000000089 (21 digits)
Make sure the numbers are close to each other as possible, with 1 zero (or 2) in between:
-> 1.230045670089 (13 digits by doing -> (123 * 10e-3) + (45.67 * 10e-7) + 0.000000000089)
🔹 This script contains examples of calculated values, % change, SMA, RMA and RSI.
These values need to be calculated from HTF close data at current TF (timeframe).
This gives challenges. For example the SMA / %change is not a problem (same values at 1h TF from Daily data).
RMA , RSI is not so easy though...
Daily values are rather similar on a 2-3h TF, but 1h TF and lower is quite different.
At the moment I haven't figured out why, if someone has an idea, don't hesitate to share.
The main goal of this publication is 'composite tickers ~ request.security()' though.
🔹 When a ticker value changes substantially (x10, x100), the multiply number needs to be adjusted accordingly.
🔶 SETTINGS
SHOW SETS
SET
• Length : length of SMA, RMA and RSI
• HTF : Higher TimeFrame (default Daily)
TABLE
• Size table : \ _ Self-explanatory
• Include exchange name : /
• Sort : If exchange names are shown, the exchanges will be sorted first
COLOURS
• CH%
• RSI
• SMA (RMA)
DEBUG
Remember t46 , T16 ,... ?
This can be used for debugging/checking
ALWAYS DISABLE " sort " when doing so.
Example:
Set string -> T1 (tickers FIL, CAKE, SOL)
(Numbers are slightly different due to time passing by between screen captures)
Placing your tickers at the side panel makes it easy to compare with the printed label below the table (right side, 332201415014.45 ),
together with the line T1 in the script:
t1 = 'BINANCE:FILUSDT' , n1 = 10e10, r1 = 4, t2 = 'BINANCE:CAKEUSDT' , n2 = 10e5 , r2 = 3, t3 = 'BINANCE:SOLUSDT' , r3 = 2 // T1
FIL : 3.322
CAKE: 1.415
SOL : 14.56
Now it is easy to check whether the tickers are placed close enough to each other, with 1-2 zero's in between.
If you want to check a specific ticker, use " Show Ticker" , see out initial example:
Set string -> T16
Show ticker -> 46 (in the code -> t46 = 'BINANCE:MTLUSDT')
(Set at 0 to disable " check string " and NONE to disable " Set string ")
-> Debug/check/set away! 😀
🔶 OTHER TECHNIQUES
• REGEX ( Regular expression ) and str.match() is used to delete the exchange name from the ticker, in other words, everything before ":" is deleted by following regex:
exch(t) => incl_exch ? t : str.match(t, "(?<=:) +")
• To sort, array.sort_indices() is used (line 675 in the code), just as in my first "sort" publication Sort array alphabetically - educational
aSort = arrT.copy()
sort_Indices = array.sort_indices(id= aSort, order= order.ascending)
• Numbers and text colour will adjust automatically when switching between light/dark mode by using chart.fg_color / chart.bg_color
🔹 DISCLAIMER
Please don't ask me for custom screeners, thank you.
3 Fib EMAs To Scalp Them AllThe "3 Fib EMAs To Scalp Them All" was made in order to clear up when we should look for shorts, longs, or walk away. Also it can alert you when a trend starts, or when there is a possible reversal. I use it for scalping/day trading in 5m-1h timeframes.
1. EMAs: By default, the indicator uses Fibonacci numbers (21, 55, 233), but you can change them.
2. Color Changes: The color of the Micro EMA line changes depending on its relation to the Mid and Macro EMAs.
When Micro EMA < Mid < Macro EMA, it turns red, indicating a potential bearish trend - that's when you should look for shorts
When Micro EMA > Mid > Macro EMA, it turns green, indicating a potential bullish trend - that's when you should look for longs
A white Micro EMA is when you need to take some rest, enjoy your coffee, and avoid overtrading.
3. Signals: The indicator provides visual signals in the form of diamonds and crosses and corresponding alert signals.
A red diamond above the bar signals a potential beginning of a downtrend
A red cross above the bar signals the end of the downtrend and can be used as a signal for a possible reversal up/breakout.
A green diamond below the bar signals a potential beginning of a downtrend,
A green cross below the bar signals the end of the uptrend and can be used as a signal for a possible reversal down/breakout.
4. Alerts: For algo traders and people who prefer to stay away from the monitor... there are alerts for every signal.
Friendly note: Don't blindly follow the signals for your long and short entries. The signals only pop up when the EMA cross value gets a confirmation. A smart move would be to wait for a retracement to the EMA line and use momentum indicators like market cipher B to pinpoint those ideal entry points.
Quinn-Fernandes Fourier Transform of Filtered Price [Loxx]Down the Rabbit Hole We Go: A Deep Dive into the Mysteries of Quinn-Fernandes Fast Fourier Transform and Hodrick-Prescott Filtering
In the ever-evolving landscape of financial markets, the ability to accurately identify and exploit underlying market patterns is of paramount importance. As market participants continuously search for innovative tools to gain an edge in their trading and investment strategies, advanced mathematical techniques, such as the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter, have emerged as powerful analytical tools. This comprehensive analysis aims to delve into the rich history and theoretical foundations of these techniques, exploring their applications in financial time series analysis, particularly in the context of a sophisticated trading indicator. Furthermore, we will critically assess the limitations and challenges associated with these transformative tools, while offering practical insights and recommendations for overcoming these hurdles to maximize their potential in the financial domain.
Our investigation will begin with a comprehensive examination of the origins and development of both the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter. We will trace their roots from classical Fourier analysis and time series smoothing to their modern-day adaptive iterations. We will elucidate the key concepts and mathematical underpinnings of these techniques and demonstrate how they are synergistically used in the context of the trading indicator under study.
As we progress, we will carefully consider the potential drawbacks and challenges associated with using the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter as integral components of a trading indicator. By providing a critical evaluation of their computational complexity, sensitivity to input parameters, assumptions about data stationarity, performance in noisy environments, and their nature as lagging indicators, we aim to offer a balanced and comprehensive understanding of these powerful analytical tools.
In conclusion, this in-depth analysis of the Quinn-Fernandes Fourier Transform and the Hodrick-Prescott Filter aims to provide a solid foundation for financial market participants seeking to harness the potential of these advanced techniques in their trading and investment strategies. By shedding light on their history, applications, and limitations, we hope to equip traders and investors with the knowledge and insights necessary to make informed decisions and, ultimately, achieve greater success in the highly competitive world of finance.
█ Fourier Transform and Hodrick-Prescott Filter in Financial Time Series Analysis
Financial time series analysis plays a crucial role in making informed decisions about investments and trading strategies. Among the various methods used in this domain, the Fourier Transform and the Hodrick-Prescott (HP) Filter have emerged as powerful techniques for processing and analyzing financial data. This section aims to provide a comprehensive understanding of these two methodologies, their significance in financial time series analysis, and their combined application to enhance trading strategies.
█ The Quinn-Fernandes Fourier Transform: History, Applications, and Use in Financial Time Series Analysis
The Quinn-Fernandes Fourier Transform is an advanced spectral estimation technique developed by John J. Quinn and Mauricio A. Fernandes in the early 1990s. It builds upon the classical Fourier Transform by introducing an adaptive approach that improves the identification of dominant frequencies in noisy signals. This section will explore the history of the Quinn-Fernandes Fourier Transform, its applications in various domains, and its specific use in financial time series analysis.
History of the Quinn-Fernandes Fourier Transform
The Quinn-Fernandes Fourier Transform was introduced in a 1993 paper titled "The Application of Adaptive Estimation to the Interpolation of Missing Values in Noisy Signals." In this paper, Quinn and Fernandes developed an adaptive spectral estimation algorithm to address the limitations of the classical Fourier Transform when analyzing noisy signals.
The classical Fourier Transform is a powerful mathematical tool that decomposes a function or a time series into a sum of sinusoids, making it easier to identify underlying patterns and trends. However, its performance can be negatively impacted by noise and missing data points, leading to inaccurate frequency identification.
Quinn and Fernandes sought to address these issues by developing an adaptive algorithm that could more accurately identify the dominant frequencies in a noisy signal, even when data points were missing. This adaptive algorithm, now known as the Quinn-Fernandes Fourier Transform, employs an iterative approach to refine the frequency estimates, ultimately resulting in improved spectral estimation.
Applications of the Quinn-Fernandes Fourier Transform
The Quinn-Fernandes Fourier Transform has found applications in various fields, including signal processing, telecommunications, geophysics, and biomedical engineering. Its ability to accurately identify dominant frequencies in noisy signals makes it a valuable tool for analyzing and interpreting data in these domains.
For example, in telecommunications, the Quinn-Fernandes Fourier Transform can be used to analyze the performance of communication systems and identify interference patterns. In geophysics, it can help detect and analyze seismic signals and vibrations, leading to improved understanding of geological processes. In biomedical engineering, the technique can be employed to analyze physiological signals, such as electrocardiograms, leading to more accurate diagnoses and better patient care.
Use of the Quinn-Fernandes Fourier Transform in Financial Time Series Analysis
In financial time series analysis, the Quinn-Fernandes Fourier Transform can be a powerful tool for isolating the dominant cycles and frequencies in asset price data. By more accurately identifying these critical cycles, traders can better understand the underlying dynamics of financial markets and develop more effective trading strategies.
The Quinn-Fernandes Fourier Transform is used in conjunction with the Hodrick-Prescott Filter, a technique that separates the underlying trend from the cyclical component in a time series. By first applying the Hodrick-Prescott Filter to the financial data, short-term fluctuations and noise are removed, resulting in a smoothed representation of the underlying trend. This smoothed data is then subjected to the Quinn-Fernandes Fourier Transform, allowing for more accurate identification of the dominant cycles and frequencies in the asset price data.
By employing the Quinn-Fernandes Fourier Transform in this manner, traders can gain a deeper understanding of the underlying dynamics of financial time series and develop more effective trading strategies. The enhanced knowledge of market cycles and frequencies can lead to improved risk management and ultimately, better investment performance.
The Quinn-Fernandes Fourier Transform is an advanced spectral estimation technique that has proven valuable in various domains, including financial time series analysis. Its adaptive approach to frequency identification addresses the limitations of the classical Fourier Transform when analyzing noisy signals, leading to more accurate and reliable analysis. By employing the Quinn-Fernandes Fourier Transform in financial time series analysis, traders can gain a deeper understanding of the underlying financial instrument.
Drawbacks to the Quinn-Fernandes algorithm
While the Quinn-Fernandes Fourier Transform is an effective tool for identifying dominant cycles and frequencies in financial time series, it is not without its drawbacks. Some of the limitations and challenges associated with this indicator include:
1. Computational complexity: The adaptive nature of the Quinn-Fernandes Fourier Transform requires iterative calculations, which can lead to increased computational complexity. This can be particularly challenging when analyzing large datasets or when the indicator is used in real-time trading environments.
2. Sensitivity to input parameters: The performance of the Quinn-Fernandes Fourier Transform is dependent on the choice of input parameters, such as the number of harmonic periods, frequency tolerance, and Hodrick-Prescott filter settings. Choosing inappropriate parameter values can lead to inaccurate frequency identification or reduced performance. Finding the optimal parameter settings can be challenging, and may require trial and error or a more sophisticated optimization process.
3. Assumption of stationary data: The Quinn-Fernandes Fourier Transform assumes that the underlying data is stationary, meaning that its statistical properties do not change over time. However, financial time series data is often non-stationary, with changing trends and volatility. This can limit the effectiveness of the indicator and may require additional preprocessing steps, such as detrending or differencing, to ensure the data meets the assumptions of the algorithm.
4. Limitations in noisy environments: Although the Quinn-Fernandes Fourier Transform is designed to handle noisy signals, its performance may still be negatively impacted by significant noise levels. In such cases, the identification of dominant frequencies may become less reliable, leading to suboptimal trading signals or strategies.
5. Lagging indicator: As with many technical analysis tools, the Quinn-Fernandes Fourier Transform is a lagging indicator, meaning that it is based on past data. While it can provide valuable insights into historical market dynamics, its ability to predict future price movements may be limited. This can result in false signals or late entries and exits, potentially reducing the effectiveness of trading strategies based on this indicator.
Despite these drawbacks, the Quinn-Fernandes Fourier Transform remains a valuable tool for financial time series analysis when used appropriately. By being aware of its limitations and adjusting input parameters or preprocessing steps as needed, traders can still benefit from its ability to identify dominant cycles and frequencies in financial data, and use this information to inform their trading strategies.
█ Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
1. The first term represents the deviation of the data from the trend.
2. The second term represents the smoothness of the trend.
3. λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
Another significant advantage of the HP Filter is its ability to adapt to changes in the underlying trend. This feature makes it particularly well-suited for analyzing financial time series, which often exhibit non-stationary behavior. By employing the HP Filter to smooth financial data, traders can more accurately identify and analyze the long-term trends that drive asset prices, ultimately leading to better-informed investment decisions.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
█ Combined Application of Fourier Transform and Hodrick-Prescott Filter
The integration of the Fourier Transform and the Hodrick-Prescott Filter in financial time series analysis can offer several benefits. By first applying the HP Filter to the financial data, traders can remove short-term fluctuations and noise, effectively isolating the underlying trend. This smoothed data can then be subjected to the Fourier Transform, allowing for the identification of dominant cycles and frequencies with greater precision.
By combining these two powerful techniques, traders can gain a more comprehensive understanding of the underlying dynamics of financial time series. This enhanced knowledge can lead to the development of more effective trading strategies, better risk management, and ultimately, improved investment performance.
The Fourier Transform and the Hodrick-Prescott Filter are powerful tools for financial time series analysis. Each technique offers unique benefits, with the Fourier Transform being adept at identifying dominant cycles and frequencies, and the HP Filter excelling at isolating long-term trends from short-term noise. By combining these methodologies, traders can develop a deeper understanding of the underlying dynamics of financial time series, leading to more informed investment decisions and improved trading strategies. As the financial markets continue to evolve, the combined application of these techniques will undoubtedly remain an essential aspect of modern financial analysis.
█ Features
Endpointed and Non-repainting
This is an endpointed and non-repainting indicator. These are crucial factors that contribute to its usefulness and reliability in trading and investment strategies. Let us break down these concepts and discuss why they matter in the context of a financial indicator.
1. Endpoint nature: An endpoint indicator uses the most recent data points to calculate its values, ensuring that the output is timely and reflective of the current market conditions. This is in contrast to non-endpoint indicators, which may use earlier data points in their calculations, potentially leading to less timely or less relevant results. By utilizing the most recent data available, the endpoint nature of this indicator ensures that it remains up-to-date and relevant, providing traders and investors with valuable and actionable insights into the market dynamics.
2. Non-repainting characteristic: A non-repainting indicator is one that does not change its values or signals after they have been generated. This means that once a signal or a value has been plotted on the chart, it will remain there, and future data will not affect it. This is crucial for traders and investors, as it offers a sense of consistency and certainty when making decisions based on the indicator's output.
Repainting indicators, on the other hand, can change their values or signals as new data comes in, effectively "repainting" the past. This can be problematic for several reasons:
a. Misleading results: Repainting indicators can create the illusion of a highly accurate or successful trading system when backtesting, as the indicator may adapt its past signals to fit the historical price data. This can lead to overly optimistic performance results that may not hold up in real-time trading.
b. Decision-making uncertainty: When an indicator repaints, it becomes challenging for traders and investors to trust its signals, as the signal that prompted a trade may change or disappear after the fact. This can create confusion and indecision, making it difficult to execute a consistent trading strategy.
The endpoint and non-repainting characteristics of this indicator contribute to its overall reliability and effectiveness as a tool for trading and investment decision-making. By providing timely and consistent information, this indicator helps traders and investors make well-informed decisions that are less likely to be influenced by misleading or shifting data.
Inputs
Source: This input determines the source of the price data to be used for the calculations. Users can select from options like closing price, opening price, high, low, etc., based on their preferences. Changing the source of the price data (e.g., from closing price to opening price) will alter the base data used for calculations, which may lead to different patterns and cycles being identified.
Calculation Bars: This input represents the number of past bars used for the calculation. A higher value will use more historical data for the analysis, while a lower value will focus on more recent price data. Increasing the number of past bars used for calculation will incorporate more historical data into the analysis. This may lead to a more comprehensive understanding of long-term trends but could also result in a slower response to recent price changes. Decreasing this value will focus more on recent data, potentially making the indicator more responsive to short-term fluctuations.
Harmonic Period: This input represents the harmonic period, which is the number of harmonics used in the Fourier Transform. A higher value will result in more harmonics being used, potentially capturing more complex cycles in the price data. Increasing the harmonic period will include more harmonics in the Fourier Transform, potentially capturing more complex cycles in the price data. However, this may also introduce more noise and make it harder to identify clear patterns. Decreasing this value will focus on simpler cycles and may make the analysis clearer, but it might miss out on more complex patterns.
Frequency Tolerance: This input represents the frequency tolerance, which determines how close the frequencies of the harmonics must be to be considered part of the same cycle. A higher value will allow for more variation between harmonics, while a lower value will require the frequencies to be more similar. Increasing the frequency tolerance will allow for more variation between harmonics, potentially capturing a broader range of cycles. However, this may also introduce noise and make it more difficult to identify clear patterns. Decreasing this value will require the frequencies to be more similar, potentially making the analysis clearer, but it might miss out on some cycles.
Number of Bars to Render: This input determines the number of bars to render on the chart. A higher value will result in more historical data being displayed, but it may also slow down the computation due to the increased amount of data being processed. Increasing the number of bars to render on the chart will display more historical data, providing a broader context for the analysis. However, this may also slow down the computation due to the increased amount of data being processed. Decreasing this value will speed up the computation, but it will provide less historical context for the analysis.
Smoothing Mode: This input allows the user to choose between two smoothing modes for the source price data: no smoothing or Hodrick-Prescott (HP) smoothing. The choice depends on the user's preference for how the price data should be processed before the Fourier Transform is applied. Choosing between no smoothing and Hodrick-Prescott (HP) smoothing will affect the preprocessing of the price data. Using HP smoothing will remove some of the short-term fluctuations from the data, potentially making the analysis clearer and more focused on longer-term trends. Not using smoothing will retain the original price fluctuations, which may provide more detail but also introduce noise into the analysis.
Hodrick-Prescott Filter Period: This input represents the Hodrick-Prescott filter period, which is used if the user chooses to apply HP smoothing to the price data. A higher value will result in a smoother curve, while a lower value will retain more of the original price fluctuations. Increasing the Hodrick-Prescott filter period will result in a smoother curve for the price data, emphasizing longer-term trends and minimizing short-term fluctuations. Decreasing this value will retain more of the original price fluctuations, potentially providing more detail but also introducing noise into the analysis.
Alets and signals
This indicator featues alerts, signals and bar coloring. You have to option to turn these on/off in the settings menu.
Maximum Bars Restriction
This indicator requires a large amount of processing power to render on the chart. To reduce overhead, the setting "Number of Bars to Render" is set to 500 bars. You can adjust this to you liking.
█ Related Indicators and Libraries
Goertzel Cycle Composite Wave
Goertzel Browser
Fourier Spectrometer of Price w/ Extrapolation Forecast
Fourier Extrapolator of 'Caterpillar' SSA of Price
Normalized, Variety, Fast Fourier Transform Explorer
Real-Fast Fourier Transform of Price Oscillator
Real-Fast Fourier Transform of Price w/ Linear Regression
Fourier Extrapolation of Variety Moving Averages
Fourier Extrapolator of Variety RSI w/ Bollinger Bands
Fourier Extrapolator of Price w/ Projection Forecast
Fourier Extrapolator of Price
STD-Stepped Fast Cosine Transform Moving Average
Variety RSI of Fast Discrete Cosine Transform
loxfft
Goertzel Cycle Composite Wave [Loxx]As the financial markets become increasingly complex and data-driven, traders and analysts must leverage powerful tools to gain insights and make informed decisions. One such tool is the Goertzel Cycle Composite Wave indicator, a sophisticated technical analysis indicator that helps identify cyclical patterns in financial data. This powerful tool is capable of detecting cyclical patterns in financial data, helping traders to make better predictions and optimize their trading strategies. With its unique combination of mathematical algorithms and advanced charting capabilities, this indicator has the potential to revolutionize the way we approach financial modeling and trading.
*** To decrease the load time of this indicator, only XX many bars back will render to the chart. You can control this value with the setting "Number of Bars to Render". This doesn't have anything to do with repainting or the indicator being endpointed***
█ Brief Overview of the Goertzel Cycle Composite Wave
The Goertzel Cycle Composite Wave is a sophisticated technical analysis tool that utilizes the Goertzel algorithm to analyze and visualize cyclical components within a financial time series. By identifying these cycles and their characteristics, the indicator aims to provide valuable insights into the market's underlying price movements, which could potentially be used for making informed trading decisions.
The Goertzel Cycle Composite Wave is considered a non-repainting and endpointed indicator. This means that once a value has been calculated for a specific bar, that value will not change in subsequent bars, and the indicator is designed to have a clear start and end point. This is an important characteristic for indicators used in technical analysis, as it allows traders to make informed decisions based on historical data without the risk of hindsight bias or future changes in the indicator's values. This means traders can use this indicator trading purposes.
The repainting version of this indicator with forecasting, cycle selection/elimination options, and data output table can be found here:
Goertzel Browser
The primary purpose of this indicator is to:
1. Detect and analyze the dominant cycles present in the price data.
2. Reconstruct and visualize the composite wave based on the detected cycles.
To achieve this, the indicator performs several tasks:
1. Detrending the price data: The indicator preprocesses the price data using various detrending techniques, such as Hodrick-Prescott filters, zero-lag moving averages, and linear regression, to remove the underlying trend and focus on the cyclical components.
2. Applying the Goertzel algorithm: The indicator applies the Goertzel algorithm to the detrended price data, identifying the dominant cycles and their characteristics, such as amplitude, phase, and cycle strength.
3. Constructing the composite wave: The indicator reconstructs the composite wave by combining the detected cycles, either by using a user-defined list of cycles or by selecting the top N cycles based on their amplitude or cycle strength.
4. Visualizing the composite wave: The indicator plots the composite wave, using solid lines for the cycles. The color of the lines indicates whether the wave is increasing or decreasing.
This indicator is a powerful tool that employs the Goertzel algorithm to analyze and visualize the cyclical components within a financial time series. By providing insights into the underlying price movements, the indicator aims to assist traders in making more informed decisions.
█ What is the Goertzel Algorithm?
The Goertzel algorithm, named after Gerald Goertzel, is a digital signal processing technique that is used to efficiently compute individual terms of the Discrete Fourier Transform (DFT). It was first introduced in 1958, and since then, it has found various applications in the fields of engineering, mathematics, and physics.
The Goertzel algorithm is primarily used to detect specific frequency components within a digital signal, making it particularly useful in applications where only a few frequency components are of interest. The algorithm is computationally efficient, as it requires fewer calculations than the Fast Fourier Transform (FFT) when detecting a small number of frequency components. This efficiency makes the Goertzel algorithm a popular choice in applications such as:
1. Telecommunications: The Goertzel algorithm is used for decoding Dual-Tone Multi-Frequency (DTMF) signals, which are the tones generated when pressing buttons on a telephone keypad. By identifying specific frequency components, the algorithm can accurately determine which button has been pressed.
2. Audio processing: The algorithm can be used to detect specific pitches or harmonics in an audio signal, making it useful in applications like pitch detection and tuning musical instruments.
3. Vibration analysis: In the field of mechanical engineering, the Goertzel algorithm can be applied to analyze vibrations in rotating machinery, helping to identify faulty components or signs of wear.
4. Power system analysis: The algorithm can be used to measure harmonic content in power systems, allowing engineers to assess power quality and detect potential issues.
The Goertzel algorithm is used in these applications because it offers several advantages over other methods, such as the FFT:
1. Computational efficiency: The Goertzel algorithm requires fewer calculations when detecting a small number of frequency components, making it more computationally efficient than the FFT in these cases.
2. Real-time analysis: The algorithm can be implemented in a streaming fashion, allowing for real-time analysis of signals, which is crucial in applications like telecommunications and audio processing.
3. Memory efficiency: The Goertzel algorithm requires less memory than the FFT, as it only computes the frequency components of interest.
4. Precision: The algorithm is less susceptible to numerical errors compared to the FFT, ensuring more accurate results in applications where precision is essential.
The Goertzel algorithm is an efficient digital signal processing technique that is primarily used to detect specific frequency components within a signal. Its computational efficiency, real-time capabilities, and precision make it an attractive choice for various applications, including telecommunications, audio processing, vibration analysis, and power system analysis. The algorithm has been widely adopted since its introduction in 1958 and continues to be an essential tool in the fields of engineering, mathematics, and physics.
█ Goertzel Algorithm in Quantitative Finance: In-Depth Analysis and Applications
The Goertzel algorithm, initially designed for signal processing in telecommunications, has gained significant traction in the financial industry due to its efficient frequency detection capabilities. In quantitative finance, the Goertzel algorithm has been utilized for uncovering hidden market cycles, developing data-driven trading strategies, and optimizing risk management. This section delves deeper into the applications of the Goertzel algorithm in finance, particularly within the context of quantitative trading and analysis.
Unveiling Hidden Market Cycles:
Market cycles are prevalent in financial markets and arise from various factors, such as economic conditions, investor psychology, and market participant behavior. The Goertzel algorithm's ability to detect and isolate specific frequencies in price data helps trader analysts identify hidden market cycles that may otherwise go unnoticed. By examining the amplitude, phase, and periodicity of each cycle, traders can better understand the underlying market structure and dynamics, enabling them to develop more informed and effective trading strategies.
Developing Quantitative Trading Strategies:
The Goertzel algorithm's versatility allows traders to incorporate its insights into a wide range of trading strategies. By identifying the dominant market cycles in a financial instrument's price data, traders can create data-driven strategies that capitalize on the cyclical nature of markets.
For instance, a trader may develop a mean-reversion strategy that takes advantage of the identified cycles. By establishing positions when the price deviates from the predicted cycle, the trader can profit from the subsequent reversion to the cycle's mean. Similarly, a momentum-based strategy could be designed to exploit the persistence of a dominant cycle by entering positions that align with the cycle's direction.
Enhancing Risk Management:
The Goertzel algorithm plays a vital role in risk management for quantitative strategies. By analyzing the cyclical components of a financial instrument's price data, traders can gain insights into the potential risks associated with their trading strategies.
By monitoring the amplitude and phase of dominant cycles, a trader can detect changes in market dynamics that may pose risks to their positions. For example, a sudden increase in amplitude may indicate heightened volatility, prompting the trader to adjust position sizing or employ hedging techniques to protect their portfolio. Additionally, changes in phase alignment could signal a potential shift in market sentiment, necessitating adjustments to the trading strategy.
Expanding Quantitative Toolkits:
Traders can augment the Goertzel algorithm's insights by combining it with other quantitative techniques, creating a more comprehensive and sophisticated analysis framework. For example, machine learning algorithms, such as neural networks or support vector machines, could be trained on features extracted from the Goertzel algorithm to predict future price movements more accurately.
Furthermore, the Goertzel algorithm can be integrated with other technical analysis tools, such as moving averages or oscillators, to enhance their effectiveness. By applying these tools to the identified cycles, traders can generate more robust and reliable trading signals.
The Goertzel algorithm offers invaluable benefits to quantitative finance practitioners by uncovering hidden market cycles, aiding in the development of data-driven trading strategies, and improving risk management. By leveraging the insights provided by the Goertzel algorithm and integrating it with other quantitative techniques, traders can gain a deeper understanding of market dynamics and devise more effective trading strategies.
█ Indicator Inputs
src: This is the source data for the analysis, typically the closing price of the financial instrument.
detrendornot: This input determines the method used for detrending the source data. Detrending is the process of removing the underlying trend from the data to focus on the cyclical components.
The available options are:
hpsmthdt: Detrend using Hodrick-Prescott filter centered moving average.
zlagsmthdt: Detrend using zero-lag moving average centered moving average.
logZlagRegression: Detrend using logarithmic zero-lag linear regression.
hpsmth: Detrend using Hodrick-Prescott filter.
zlagsmth: Detrend using zero-lag moving average.
DT_HPper1 and DT_HPper2: These inputs define the period range for the Hodrick-Prescott filter centered moving average when detrendornot is set to hpsmthdt.
DT_ZLper1 and DT_ZLper2: These inputs define the period range for the zero-lag moving average centered moving average when detrendornot is set to zlagsmthdt.
DT_RegZLsmoothPer: This input defines the period for the zero-lag moving average used in logarithmic zero-lag linear regression when detrendornot is set to logZlagRegression.
HPsmoothPer: This input defines the period for the Hodrick-Prescott filter when detrendornot is set to hpsmth.
ZLMAsmoothPer: This input defines the period for the zero-lag moving average when detrendornot is set to zlagsmth.
MaxPer: This input sets the maximum period for the Goertzel algorithm to search for cycles.
squaredAmp: This boolean input determines whether the amplitude should be squared in the Goertzel algorithm.
useAddition: This boolean input determines whether the Goertzel algorithm should use addition for combining the cycles.
useCosine: This boolean input determines whether the Goertzel algorithm should use cosine waves instead of sine waves.
UseCycleStrength: This boolean input determines whether the Goertzel algorithm should compute the cycle strength, which is a normalized measure of the cycle's amplitude.
WindowSizePast: These inputs define the window size for the composite wave.
FilterBartels: This boolean input determines whether Bartel's test should be applied to filter out non-significant cycles.
BartNoCycles: This input sets the number of cycles to be used in Bartel's test.
BartSmoothPer: This input sets the period for the moving average used in Bartel's test.
BartSigLimit: This input sets the significance limit for Bartel's test, below which cycles are considered insignificant.
SortBartels: This boolean input determines whether the cycles should be sorted by their Bartel's test results.
StartAtCycle: This input determines the starting index for selecting the top N cycles when UseCycleList is set to false. This allows you to skip a certain number of cycles from the top before selecting the desired number of cycles.
UseTopCycles: This input sets the number of top cycles to use for constructing the composite wave when UseCycleList is set to false. The cycles are ranked based on their amplitudes or cycle strengths, depending on the UseCycleStrength input.
SubtractNoise: This boolean input determines whether to subtract the noise (remaining cycles) from the composite wave. If set to true, the composite wave will only include the top N cycles specified by UseTopCycles.
█ Exploring Auxiliary Functions
The following functions demonstrate advanced techniques for analyzing financial markets, including zero-lag moving averages, Bartels probability, detrending, and Hodrick-Prescott filtering. This section examines each function in detail, explaining their purpose, methodology, and applications in finance. We will examine how each function contributes to the overall performance and effectiveness of the indicator and how they work together to create a powerful analytical tool.
Zero-Lag Moving Average:
The zero-lag moving average function is designed to minimize the lag typically associated with moving averages. This is achieved through a two-step weighted linear regression process that emphasizes more recent data points. The function calculates a linearly weighted moving average (LWMA) on the input data and then applies another LWMA on the result. By doing this, the function creates a moving average that closely follows the price action, reducing the lag and improving the responsiveness of the indicator.
The zero-lag moving average function is used in the indicator to provide a responsive, low-lag smoothing of the input data. This function helps reduce the noise and fluctuations in the data, making it easier to identify and analyze underlying trends and patterns. By minimizing the lag associated with traditional moving averages, this function allows the indicator to react more quickly to changes in market conditions, providing timely signals and improving the overall effectiveness of the indicator.
Bartels Probability:
The Bartels probability function calculates the probability of a given cycle being significant in a time series. It uses a mathematical test called the Bartels test to assess the significance of cycles detected in the data. The function calculates coefficients for each detected cycle and computes an average amplitude and an expected amplitude. By comparing these values, the Bartels probability is derived, indicating the likelihood of a cycle's significance. This information can help in identifying and analyzing dominant cycles in financial markets.
The Bartels probability function is incorporated into the indicator to assess the significance of detected cycles in the input data. By calculating the Bartels probability for each cycle, the indicator can prioritize the most significant cycles and focus on the market dynamics that are most relevant to the current trading environment. This function enhances the indicator's ability to identify dominant market cycles, improving its predictive power and aiding in the development of effective trading strategies.
Detrend Logarithmic Zero-Lag Regression:
The detrend logarithmic zero-lag regression function is used for detrending data while minimizing lag. It combines a zero-lag moving average with a linear regression detrending method. The function first calculates the zero-lag moving average of the logarithm of input data and then applies a linear regression to remove the trend. By detrending the data, the function isolates the cyclical components, making it easier to analyze and interpret the underlying market dynamics.
The detrend logarithmic zero-lag regression function is used in the indicator to isolate the cyclical components of the input data. By detrending the data, the function enables the indicator to focus on the cyclical movements in the market, making it easier to analyze and interpret market dynamics. This function is essential for identifying cyclical patterns and understanding the interactions between different market cycles, which can inform trading decisions and enhance overall market understanding.
Bartels Cycle Significance Test:
The Bartels cycle significance test is a function that combines the Bartels probability function and the detrend logarithmic zero-lag regression function to assess the significance of detected cycles. The function calculates the Bartels probability for each cycle and stores the results in an array. By analyzing the probability values, traders and analysts can identify the most significant cycles in the data, which can be used to develop trading strategies and improve market understanding.
The Bartels cycle significance test function is integrated into the indicator to provide a comprehensive analysis of the significance of detected cycles. By combining the Bartels probability function and the detrend logarithmic zero-lag regression function, this test evaluates the significance of each cycle and stores the results in an array. The indicator can then use this information to prioritize the most significant cycles and focus on the most relevant market dynamics. This function enhances the indicator's ability to identify and analyze dominant market cycles, providing valuable insights for trading and market analysis.
Hodrick-Prescott Filter:
The Hodrick-Prescott filter is a popular technique used to separate the trend and cyclical components of a time series. The function applies a smoothing parameter to the input data and calculates a smoothed series using a two-sided filter. This smoothed series represents the trend component, which can be subtracted from the original data to obtain the cyclical component. The Hodrick-Prescott filter is commonly used in economics and finance to analyze economic data and financial market trends.
The Hodrick-Prescott filter is incorporated into the indicator to separate the trend and cyclical components of the input data. By applying the filter to the data, the indicator can isolate the trend component, which can be used to analyze long-term market trends and inform trading decisions. Additionally, the cyclical component can be used to identify shorter-term market dynamics and provide insights into potential trading opportunities. The inclusion of the Hodrick-Prescott filter adds another layer of analysis to the indicator, making it more versatile and comprehensive.
Detrending Options: Detrend Centered Moving Average:
The detrend centered moving average function provides different detrending methods, including the Hodrick-Prescott filter and the zero-lag moving average, based on the selected detrending method. The function calculates two sets of smoothed values using the chosen method and subtracts one set from the other to obtain a detrended series. By offering multiple detrending options, this function allows traders and analysts to select the most appropriate method for their specific needs and preferences.
The detrend centered moving average function is integrated into the indicator to provide users with multiple detrending options, including the Hodrick-Prescott filter and the zero-lag moving average. By offering multiple detrending methods, the indicator allows users to customize the analysis to their specific needs and preferences, enhancing the indicator's overall utility and adaptability. This function ensures that the indicator can cater to a wide range of trading styles and objectives, making it a valuable tool for a diverse group of market participants.
The auxiliary functions functions discussed in this section demonstrate the power and versatility of mathematical techniques in analyzing financial markets. By understanding and implementing these functions, traders and analysts can gain valuable insights into market dynamics, improve their trading strategies, and make more informed decisions. The combination of zero-lag moving averages, Bartels probability, detrending methods, and the Hodrick-Prescott filter provides a comprehensive toolkit for analyzing and interpreting financial data. The integration of advanced functions in a financial indicator creates a powerful and versatile analytical tool that can provide valuable insights into financial markets. By combining the zero-lag moving average,
█ In-Depth Analysis of the Goertzel Cycle Composite Wave Code
The Goertzel Cycle Composite Wave code is an implementation of the Goertzel Algorithm, an efficient technique to perform spectral analysis on a signal. The code is designed to detect and analyze dominant cycles within a given financial market data set. This section will provide an extremely detailed explanation of the code, its structure, functions, and intended purpose.
Function signature and input parameters:
The Goertzel Cycle Composite Wave function accepts numerous input parameters for customization, including source data (src), the current bar (forBar), sample size (samplesize), period (per), squared amplitude flag (squaredAmp), addition flag (useAddition), cosine flag (useCosine), cycle strength flag (UseCycleStrength), past sizes (WindowSizePast), Bartels filter flag (FilterBartels), Bartels-related parameters (BartNoCycles, BartSmoothPer, BartSigLimit), sorting flag (SortBartels), and output buffers (goeWorkPast, cyclebuffer, amplitudebuffer, phasebuffer, cycleBartelsBuffer).
Initializing variables and arrays:
The code initializes several float arrays (goeWork1, goeWork2, goeWork3, goeWork4) with the same length as twice the period (2 * per). These arrays store intermediate results during the execution of the algorithm.
Preprocessing input data:
The input data (src) undergoes preprocessing to remove linear trends. This step enhances the algorithm's ability to focus on cyclical components in the data. The linear trend is calculated by finding the slope between the first and last values of the input data within the sample.
Iterative calculation of Goertzel coefficients:
The core of the Goertzel Cycle Composite Wave algorithm lies in the iterative calculation of Goertzel coefficients for each frequency bin. These coefficients represent the spectral content of the input data at different frequencies. The code iterates through the range of frequencies, calculating the Goertzel coefficients using a nested loop structure.
Cycle strength computation:
The code calculates the cycle strength based on the Goertzel coefficients. This is an optional step, controlled by the UseCycleStrength flag. The cycle strength provides information on the relative influence of each cycle on the data per bar, considering both amplitude and cycle length. The algorithm computes the cycle strength either by squaring the amplitude (controlled by squaredAmp flag) or using the actual amplitude values.
Phase calculation:
The Goertzel Cycle Composite Wave code computes the phase of each cycle, which represents the position of the cycle within the input data. The phase is calculated using the arctangent function (math.atan) based on the ratio of the imaginary and real components of the Goertzel coefficients.
Peak detection and cycle extraction:
The algorithm performs peak detection on the computed amplitudes or cycle strengths to identify dominant cycles. It stores the detected cycles in the cyclebuffer array, along with their corresponding amplitudes and phases in the amplitudebuffer and phasebuffer arrays, respectively.
Sorting cycles by amplitude or cycle strength:
The code sorts the detected cycles based on their amplitude or cycle strength in descending order. This allows the algorithm to prioritize cycles with the most significant impact on the input data.
Bartels cycle significance test:
If the FilterBartels flag is set, the code performs a Bartels cycle significance test on the detected cycles. This test determines the statistical significance of each cycle and filters out the insignificant cycles. The significant cycles are stored in the cycleBartelsBuffer array. If the SortBartels flag is set, the code sorts the significant cycles based on their Bartels significance values.
Waveform calculation:
The Goertzel Cycle Composite Wave code calculates the waveform of the significant cycles for specified time windows. The windows are defined by the WindowSizePast parameters, respectively. The algorithm uses either cosine or sine functions (controlled by the useCosine flag) to calculate the waveforms for each cycle. The useAddition flag determines whether the waveforms should be added or subtracted.
Storing waveforms in a matrix:
The calculated waveforms for the cycle is stored in the matrix - goeWorkPast. This matrix holds the waveforms for the specified time windows. Each row in the matrix represents a time window position, and each column corresponds to a cycle.
Returning the number of cycles:
The Goertzel Cycle Composite Wave function returns the total number of detected cycles (number_of_cycles) after processing the input data. This information can be used to further analyze the results or to visualize the detected cycles.
The Goertzel Cycle Composite Wave code is a comprehensive implementation of the Goertzel Algorithm, specifically designed for detecting and analyzing dominant cycles within financial market data. The code offers a high level of customization, allowing users to fine-tune the algorithm based on their specific needs. The Goertzel Cycle Composite Wave's combination of preprocessing, iterative calculations, cycle extraction, sorting, significance testing, and waveform calculation makes it a powerful tool for understanding cyclical components in financial data.
█ Generating and Visualizing Composite Waveform
The indicator calculates and visualizes the composite waveform for specified time windows based on the detected cycles. Here's a detailed explanation of this process:
Updating WindowSizePast:
The WindowSizePast is updated to ensure they are at least twice the MaxPer (maximum period).
Initializing matrices and arrays:
The matrix goeWorkPast is initialized to store the Goertzel results for specified time windows. Multiple arrays are also initialized to store cycle, amplitude, phase, and Bartels information.
Preparing the source data (srcVal) array:
The source data is copied into an array, srcVal, and detrended using one of the selected methods (hpsmthdt, zlagsmthdt, logZlagRegression, hpsmth, or zlagsmth).
Goertzel function call:
The Goertzel function is called to analyze the detrended source data and extract cycle information. The output, number_of_cycles, contains the number of detected cycles.
Initializing arrays for waveforms:
The goertzel array is initialized to store the endpoint Goertzel.
Calculating composite waveform (goertzel array):
The composite waveform is calculated by summing the selected cycles (either from the user-defined cycle list or the top cycles) and optionally subtracting the noise component.
Drawing composite waveform (pvlines):
The composite waveform is drawn on the chart using solid lines. The color of the lines is determined by the direction of the waveform (green for upward, red for downward).
To summarize, this indicator generates a composite waveform based on the detected cycles in the financial data. It calculates the composite waveforms and visualizes them on the chart using colored lines.
█ Enhancing the Goertzel Algorithm-Based Script for Financial Modeling and Trading
The Goertzel algorithm-based script for detecting dominant cycles in financial data is a powerful tool for financial modeling and trading. It provides valuable insights into the past behavior of these cycles. However, as with any algorithm, there is always room for improvement. This section discusses potential enhancements to the existing script to make it even more robust and versatile for financial modeling, general trading, advanced trading, and high-frequency finance trading.
Enhancements for Financial Modeling
Data preprocessing: One way to improve the script's performance for financial modeling is to introduce more advanced data preprocessing techniques. This could include removing outliers, handling missing data, and normalizing the data to ensure consistent and accurate results.
Additional detrending and smoothing methods: Incorporating more sophisticated detrending and smoothing techniques, such as wavelet transform or empirical mode decomposition, can help improve the script's ability to accurately identify cycles and trends in the data.
Machine learning integration: Integrating machine learning techniques, such as artificial neural networks or support vector machines, can help enhance the script's predictive capabilities, leading to more accurate financial models.
Enhancements for General and Advanced Trading
Customizable indicator integration: Allowing users to integrate their own technical indicators can help improve the script's effectiveness for both general and advanced trading. By enabling the combination of the dominant cycle information with other technical analysis tools, traders can develop more comprehensive trading strategies.
Risk management and position sizing: Incorporating risk management and position sizing functionality into the script can help traders better manage their trades and control potential losses. This can be achieved by calculating the optimal position size based on the user's risk tolerance and account size.
Multi-timeframe analysis: Enhancing the script to perform multi-timeframe analysis can provide traders with a more holistic view of market trends and cycles. By identifying dominant cycles on different timeframes, traders can gain insights into the potential confluence of cycles and make better-informed trading decisions.
Enhancements for High-Frequency Finance Trading
Algorithm optimization: To ensure the script's suitability for high-frequency finance trading, optimizing the algorithm for faster execution is crucial. This can be achieved by employing efficient data structures and refining the calculation methods to minimize computational complexity.
Real-time data streaming: Integrating real-time data streaming capabilities into the script can help high-frequency traders react to market changes more quickly. By continuously updating the cycle information based on real-time market data, traders can adapt their strategies accordingly and capitalize on short-term market fluctuations.
Order execution and trade management: To fully leverage the script's capabilities for high-frequency trading, implementing functionality for automated order execution and trade management is essential. This can include features such as stop-loss and take-profit orders, trailing stops, and automated trade exit strategies.
While the existing Goertzel algorithm-based script is a valuable tool for detecting dominant cycles in financial data, there are several potential enhancements that can make it even more powerful for financial modeling, general trading, advanced trading, and high-frequency finance trading. By incorporating these improvements, the script can become a more versatile and effective tool for traders and financial analysts alike.
█ Understanding the Limitations of the Goertzel Algorithm
While the Goertzel algorithm-based script for detecting dominant cycles in financial data provides valuable insights, it is important to be aware of its limitations and drawbacks. Some of the key drawbacks of this indicator are:
Lagging nature:
As with many other technical indicators, the Goertzel algorithm-based script can suffer from lagging effects, meaning that it may not immediately react to real-time market changes. This lag can lead to late entries and exits, potentially resulting in reduced profitability or increased losses.
Parameter sensitivity:
The performance of the script can be sensitive to the chosen parameters, such as the detrending methods, smoothing techniques, and cycle detection settings. Improper parameter selection may lead to inaccurate cycle detection or increased false signals, which can negatively impact trading performance.
Complexity:
The Goertzel algorithm itself is relatively complex, making it difficult for novice traders or those unfamiliar with the concept of cycle analysis to fully understand and effectively utilize the script. This complexity can also make it challenging to optimize the script for specific trading styles or market conditions.
Overfitting risk:
As with any data-driven approach, there is a risk of overfitting when using the Goertzel algorithm-based script. Overfitting occurs when a model becomes too specific to the historical data it was trained on, leading to poor performance on new, unseen data. This can result in misleading signals and reduced trading performance.
Limited applicability:
The Goertzel algorithm-based script may not be suitable for all markets, trading styles, or timeframes. Its effectiveness in detecting cycles may be limited in certain market conditions, such as during periods of extreme volatility or low liquidity.
While the Goertzel algorithm-based script offers valuable insights into dominant cycles in financial data, it is essential to consider its drawbacks and limitations when incorporating it into a trading strategy. Traders should always use the script in conjunction with other technical and fundamental analysis tools, as well as proper risk management, to make well-informed trading decisions.
█ Interpreting Results
The Goertzel Cycle Composite Wave indicator can be interpreted by analyzing the plotted lines. The indicator plots two lines: composite waves. The composite wave represents the composite wave of the price data.
The composite wave line displays a solid line, with green indicating a bullish trend and red indicating a bearish trend.
Interpreting the Goertzel Cycle Composite Wave indicator involves identifying the trend of the composite wave lines and matching them with the corresponding bullish or bearish color.
█ Conclusion
The Goertzel Cycle Composite Wave indicator is a powerful tool for identifying and analyzing cyclical patterns in financial markets. Its ability to detect multiple cycles of varying frequencies and strengths make it a valuable addition to any trader's technical analysis toolkit. However, it is important to keep in mind that the Goertzel Cycle Composite Wave indicator should be used in conjunction with other technical analysis tools and fundamental analysis to achieve the best results. With continued refinement and development, the Goertzel Cycle Composite Wave indicator has the potential to become a highly effective tool for financial modeling, general trading, advanced trading, and high-frequency finance trading. Its accuracy and versatility make it a promising candidate for further research and development.
█ Footnotes
What is the Bartels Test for Cycle Significance?
The Bartels Cycle Significance Test is a statistical method that determines whether the peaks and troughs of a time series are statistically significant. The test is named after its inventor, George Bartels, who developed it in the mid-20th century.
The Bartels test is designed to analyze the cyclical components of a time series, which can help traders and analysts identify trends and cycles in financial markets. The test calculates a Bartels statistic, which measures the degree of non-randomness or autocorrelation in the time series.
The Bartels statistic is calculated by first splitting the time series into two halves and calculating the range of the peaks and troughs in each half. The test then compares these ranges using a t-test, which measures the significance of the difference between the two ranges.
If the Bartels statistic is greater than a critical value, it indicates that the peaks and troughs in the time series are non-random and that there is a significant cyclical component to the data. Conversely, if the Bartels statistic is less than the critical value, it suggests that the peaks and troughs are random and that there is no significant cyclical component.
The Bartels Cycle Significance Test is particularly useful in financial analysis because it can help traders and analysts identify significant cycles in asset prices, which can in turn inform investment decisions. However, it is important to note that the test is not perfect and can produce false signals in certain situations, particularly in noisy or volatile markets. Therefore, it is always recommended to use the test in conjunction with other technical and fundamental indicators to confirm trends and cycles.
Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
1. The first term represents the deviation of the data from the trend.
2. The second term represents the smoothness of the trend.
3. λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
ZigZag█ OVERVIEW
This library is a Pine Script™ programmer’s tool containing custom user-defined types and functions to calculate Zig Zag indicators within their scripts. It is not a stand-alone indicator.
Pine Script™ libraries are publications that contain reusable code for importing into Pine Script™ indicators, strategies, and other libraries. For more information on libraries and incorporating them into your scripts, see the Libraries section of the Pine Script™ User Manual .
█ CONCEPTS
Zig Zag
Zig Zag is a popular indicator that filters out minor price fluctuations to denoise data and emphasize trends. Traders commonly use Zig Zag for trend confirmation, identifying potential support and resistance, and pattern detection. It is formed by identifying significant local high and low points in alternating order and connecting them with straight lines, omitting all other data points from their output. There are several ways to calculate the Zig Zag's data points and the conditions by which its direction changes. This script uses pivots as the data points, which are the highest or lowest values over a defined number of bars before and after them. The direction only reverses when a newly formed pivot deviates from the last Zig Zag point in the opposite direction by an amount greater than or equal to a specified percentage.
To learn more about Zig Zag and how to calculate it, see this entry from the Help Center.
█ FOR Pine Script™ CODERS
Notes
This script's architecture utilizes user-defined types (UDTs) to create custom objects which are the equivalent of variables containing multiple parts, each able to hold independent values of different types . UDTs are the newest addition to Pine Script™ and the most advanced feature the language has seen to date. The feature's introduction creates a new runway for experienced coders to push the boundaries of Pine. We recommend that newcomers to the language explore the basics first before diving into UDTs and objects.
Demonstration Code
Our example code shows a simple use case by displaying a Zig Zag with user-defined settings. A new ZigZag object is instantiated on the first bar using a Settings object to control its attributes. The fields for the Settings object are declared using variables assigned to input.* functions, allowing control of the field values from the script's settings. The `update()` function is invoked on each bar to update the ZigZag object's fields and create new lines and labels when required.
Look first. Then leap.
█ TYPES
This library contains the following types:
Settings
Provides calculation and display attributes to ZigZag objects.
Fields:
devThreshold : The minimum percentage deviation from a point before the ZigZag will change direction.
depth : The number of bars required for pivot detection.
lineColor : Line color.
extendLast : Condition allowing a line to connect the most recent pivot with the current close.
displayReversalPrice : Condition to display the pivot price in the pivot label.
displayCumulativeVolume : Condition to display the cumulative volume for the pivot segment in the pivot label.
displayReversalPriceChange : Condition to display the change in price or percent from the previous pivot in the pivot label.
differencePriceMode : Reversal change display mode. Options are "Absolute" or "Percent".
draw : Condition to display lines and labels.
Point
A coordinate containing time and price information.
Fields:
tm : A value in UNIX time.
price : A value on the Y axis (price).
Pivot
A level of significance used to determine directional movement or potential support and resistance.
Fields:
ln : A line object connecting the `start` and `end` Point objects.
lb : A label object to display pivot values.
isHigh : A condition to determine if the pivot is a pivot high.
vol : Volume for the pivot segment.
start : The coordinate of the previous Point.
end : The coordinate of the current Point.
ZigZag
An object to maintain Zig Zag settings, pivots, and volume.
Fields:
settings : Settings object to provide calculation and display attributes.
pivots : An array of Pivot objects.
sumVol : The volume sum for the pivot segment.
extend : Pivot object used to project a line from the last pivot to the last bar.
█ FUNCTIONS
This library contains the following functions:
lastPivot(this)
Returns the last Pivot of `this` ZigZag if there is at least one Pivot to return, and `na` otherwise.
Parameters:
this : (series ZigZag) A ZigZag object.
Returns: (Pivot) The last Pivot in the ZigZag.
update(this)
Updates `this` ZigZag object with new pivots, volume, lines, labels.
Parameters:
this : (series ZigZag) a ZigZag object.
Returns: (bool) true if a new Zig Zag line is found or the last Zig Zag line has changed.
newInstance(settings)
Instantiates a new ZigZag object with `settings`. If no settings are provided, a default ZigZag object is created.
Parameters:
settings : (series Settings) A Settings object.
Returns: (ZigZag) A new ZigZag instance.
Multi Delta-Agnostic Correlation Coefficient (tartigradia)Display three DACC plots simultaneously, to visualize both directional (up on top, down at bottom) and adirectional DACC (in the middle) simultaneously.
Delta Agnostic Correlation calculates a correlation between two symbols based only on the sign of their changes using a Sign Test (en.m.wikipedia.org), regardless of the amplitude of price change. Compared to a standard Pearson correlation (quantitative test), Sign Test correlations (discrete test) are highly sensitive to directional change with 0 lag, at the expense of lacking sensitivity to quantity correlation (ie, it does not matter if changes are big or small).
Hence, this Delta-Agnostic Correlation Coefficient (DCC or DACC) indicator is better used to detect early changes in correlations, and then confirmation with a typical Pearson correlation or a non-parametric Spearman test or Mutual Information (all three are quantitative tests, hence accounting for quantity and not just direction) can allow to be more sensitive to quantities too and hence be a robust combination to demonstrate strong correlations both in direction and amplitude.
Adequate statistical significance testing, using a two-sided binomial statistical test, is also implemented. Note however that one assumption of the sign test may here be violated: independence of observations for each symbol. If you assume the market is not acting on a random walk, then there is a temporal autocorrelation, and this biases the sign test. However, in practice, the test works well enough.
The directional variants of the test allow to test the correlation hypothesis only if the index symbol goes into one direction. For example, if we suspect that the index symbol is correlated with the current symbol but only when the index symbol is bullish, we can select "Up" to test this hypothesis. Note that given the specificities of how directional and adirectional tests differ in how they work, the default fill is different: zero-value fill for adirectional test to simulate how price action tend to lose momentum during market close periods, previous DCC_MA (= no change in DCC value) during both market close periods and when the direction is opposite for the directional variants of the test, so that while the market is moving opposite, we don't lose the statistical significance built up to now, otherwise it would be nonsensical (for the directional tests).
For more information on the theory behind, see the original DACC indicator, which is the same script but with only one plot:
SPX Fair Value Bands V2An updated version of the SPX Fair Value Bands script from dharmatech and based on the net liquidity concept by MaxJAnderson .
Now with full customization of parameters through the settings (Dialog Box) and allowing the options to the use of
1) Standard Bands based on Offsets of the Fair Value
2) Bollinger Bands
3) Keltner Channels
to better capture buy/sell areas rather than relying on noisy unreliably (and unevenly) updated data from the Treasury/Fed.
==================================
Net Liquidity's importance in the new post-COVID QE to QT regime as described MaxJAnderson
----------------
" In past cycles, size of Fed's balance sheet changed a lot, while TGA and RRP changed relatively little. So size of balance sheet roughly equated Net Liquidity.
(The Treasury General Account) TGA and (Reverse Repo) RRP didn't matter. They were rounding errors by comparison.
But starting in 2020, relative changes in TGA and RRP have been THREE TIMES LARGER than the change in size of the Fed's balance sheet. As result, changes in TGA and RRP have taken over as the primary drivers Net Liquidity.
This is new, and changes the game significantly. Again - the size of the Fed's balance sheet doesn't matter.
What matters is the portion of it that's available to circulate in the economy (Net Liquidity).
And ever since 2020, the Treasury and Reverse Repo have become what controls that. Not the size of Fed's balance sheet.
----------------
The idea that follows is simple,short when $SPX reaches extreme levels of overvaluation, and close out when SPX returns to being undervalued. Here's the formulas I currently use to determine fair value:
Fair Value = (Fed Bal Sheet - TGA - RRP)/1.1 - 1625
And here's the trading rules I currently follow:
Short when diff of $SPX - Fair Value > 350
Close when diff of $SPX - Fair Value < 150
When one of these rules is triggered upon market close on a given day, trades are entered at open of the following day "
Directional Index Macro IndicatorWhat is This For?
The default settings for this indicator are for BINANCE:BTCUSDT and intended to be used on the 3D timeframe to identify market trends. This indicator does a great job identifying whether the market is bullish, bearish, or consolidating. This can also work well on lower time frames to help identify when a trend is strong or when it's reversing.
Directional Index Rate of Change
Core to this indicator is the rate at which DI+ and DI- are moving away or towards each other. This is called The Rate of Change (ROC). "The ROC length dictates how many bars back you want to compare to the current bar to see how much it has changed. It is calculated like this:
(source - source /source ) * 100"
The rate of change is smoothed using an EMA. A shorter EMA length will cause the ROC to flip back and forth between positive and negative while a larger EMA length will cause the ROC to change less often. Since the rate of change is used to indicate periods of 'consolidation', you want to find a setting that doesn't flip back and forth too often. Between the DI+ and DI- is a blue centerline. Offset from this centerline is a channel that is used to filter out false crosses of the DI+ and DI-. Sometimes, the DI+ and DI- lines will come together in this channel and cross momentarily before resuming the direction prior to the cross. When this happens, you don't want to flip your bias too soon. The wider the channel, the later the indicator will signal a DI reversal. A narrower channel will call it sooner but risks being more choppy and indicating a false cross.
Indicator Status Line
This indicator has 4 values in the status line (in order):
DI+
DI-
Distance between DI+ and DI-
DI Rate of Change ( how quickly are DI+ and DI- moving away or towards center )
Indicator Plots
This indicator plots DI+ (green), DI- (red), and a center channel between DI- and DI+. Across the top of the indicator, red and green triangles indicate the market trend while the background changes to show whether the price is in an impulse wave or consolidating. This makes up 4 possible scenarios:
Bullish impulse wave ( green triangle up + green background )
Bullish consolidation ( green triangle up + yellow background )
Bearish impulse wave ( red triangle down + red background )
Bearish consolidation ( red triangle down + yellow background )
Summary
Combined with support and resistance levels, volume, and your other favorite indicators, this can be a useful tool for validating that your entries are not going against the trend.
Disclaimer
This is not financial advice. Do not take trades only based on the DI+ and DI- crossing. Always use multiple indicators to validate your entries and never take a trade when you aren’t emotionally grounded. Have a plan. Stick to the plan.
The screenshot for this strategy is of a manual historical review of BTC on the 3 day chart. The indicator was built to try and mimic the chart above. You’ll see that it nails it sometimes, is a little late sometimes, and chops around between consolidation and impulse waves when it should stay in consolidation. Share your settings if you are able to improve the choppiness without sacrificing catching the reversals early.
CHS Zig ZagCHS ZigZag stands for Changeable Source ZigZag
The original ZigZag indicator offered by TradingView doesn't have the ability to measure the tips and troughs based on closing prices (line chart), however, this indicator is capable of receiving an input from user that determines the price source used for further calculations.
The default inputs of the original ZigZag indicator have been also changed in order to make it adapt to pivots formed on line chart but users can change arbitrarily.
Swing EMAWhat is Swing EMA?
Swing EMA is an exponential moving average crossover-based indicator used for low-risk directional trading.
it's used for different types of Ema 20,50,100 and 200, 3 of them are plotted on chat 20,100,200.
100 and 200 Ema is used for showing support and resistance and it contains highlights area between them and its change color according to market crossover condition.
20 moving average is used for knowing Market Behaviour and changing its color according to crossover conditions of 50 and 20 Ema.
How does it work?
It contains 4 different types of moving averages 20,50,100, 200 out of 3 are plotted on the chart.
20 Ema is used for knowing current market behavior. Its changes its color based on the crossover of 50 Ema and 20 Ema, if 20 Ema is higher than 50 Ema then it changes its color to green, and its opposites are changed their color to red when 20 Ema is lower than 50 Ema.
100 and 200 Ema used as a support and resistance and is also contain highlighted areas between them its change their color based on the crossover if 100 Ema is higher than 200 Ema a then both of them are going to change color to Green and as an opposite, if 200 Ema is higher then 100 Ema is going to change its color to red.
So in simple word 100 and 200 Ema is used as support and resistance zone and 20 Ema is used to know current market behavior.
How to use it?
It is very easy to understand by looking at the example I gave where are the two different types of phrases. phrase bull phrase and bear phrase so 100 and 200 Ema is used as a support and resistance and to tell you which phrase is currently on the market on example there is a bull phrase on the left side and bear phrase on the right side by using your technical analysis you can find out a really good spot to buy your stocks on a bull phrase and too short on the bear phrase. 20 Ema is used as a knowing the current market behavior it doesn't make any difference on buying or selling as much as 100 Ema and 200 Ema.
Tips
Don't trade against the market.
Try trade on trending stocks rather than sideways stock.
The higher the area between 100 Ema and 200 Ema is the stronger the phrase.
Do Backtesting before real trading.
Enjoy Trading.
Volume-based Support & Resistance ZonesThe new and improved Support & Resistance Zones indicator is here. This indicator is based on high volume at fractal lows or fractal highs with the zones based on the size of the wick for that timeframe’s candle.
This helps traders visualize which price levels are of the most significance for either reversals or continuation of the trend when zones are broken and then re-tested.
Original script is thanks to synapticex and additional modifications is thanks to Lij_MC. Credit to both of them for most of the logic behind this script.
Since then I have made many changes to this script as noted below:
Changed default S/R lines from plots to lines, and gave option to user to change between solid line, dashed line, or dotted line for both S/R lines.
Added additional time frame and gave more TF options for TF1 other than current TF. Now you will have 4 time frames to plot S/R zones from.
Gave user option to easily change line thickness for all S/R lines.
Made it easier to change colors of S/R lines and zones by consolidating the options under settings (rather than under style).
Added extensions to active SR Zones to extend all the way right.
Added option to extend or not extend the previous S/R zones up to next S/R zone.
Added optional time frame labels to active S/R zones, with left and right options as well as option to adjust how far to the right label is set.
Fixed issue where the higher time frame S/R zone was not properly starting from the high/low of fractal. Now any higher time frame S/R will begin exactly at the High/Low points. Note that this may not work perfectly on stocks and if a fractal high/low is too many bars in the past, it will revert to a default max bars back to avoid script errors.
Added to script a function that will prevent S/R zones from lower time frames displaying while on a higher time frame. This helps clean up the chart quite a bit.
Created arrays for each time frame's boxes and lines so that the number of S/R zones can be controlled for each time frame and limit memory consumption.
New alert options added and customized alert messages.
- The way this indicator works is it looks for fractal highs or fractal lows with volume that pierces above the volume's Moving Average. This moving average value can be modified in the settings for each time frame.
- The fractal highs will be confirmed with 3 successive higher highs followed by 2 successive lower highs and vice versa for the fractal lows.
- The zone is created from the fractal high/low and the close of the candle for whatever time frame you selected. The bigger the zone, the more significant that zone is.
- You can disable any zone, change the zones to show lines only, and modify all the colors, transparencies, and thickness of lines for all the zones.
- To create alerts, you first want to enable the types of alerts you want for each time frame in the indicator's settings. Then after you apply changes, right click on one of the zones on the chart, and click "Add Alert on Vol S/R Zones". You do not need to add a title as the correct alert messages are already built-in.
- More changes will be coming in the future!
I hope you find this indicator useful, if so please give it a thumbs up!
If you have any suggestions or features you would like to see, just let me know in the comment section. Thanks and enjoy!
