Historical Correlation [LuxAlgo]The Historical Correlation tool aims to provide the historical correlation coefficients of up to 10 pairs of user-defined tickers starting from a user-defined point in time.
Users can choose to display the historical values as lines or the most recent correlation values as a heat map.
🔶 USAGE
This tool provides historical correlation coefficients, the correlation coefficient between two assets highlight their linear relationship and is always within the range (-1, 1).
It is a simple and easy to use statistical tool, with the following interpretation:
Positive correlation (values close to +1.0): the two assets move in sync, they rise and fall at the same time.
Negative correlation (values close to -1.0): the two assets move in opposite directions: when one goes up, the other goes down and vice versa.
No correlation (values close to 0): the two assets move independently.
The user must confirm the selection of the anchor point in order for the tool to be executed; this can be done directly on the chart by clicking on any bar, or via the date field in the settings panel.
For the parameter Anchor period , the user can choose between the following values NONE, HOURLY, DAILY, WEEKLY, MONTHLY, QUARTERLY and YEARLY. If NONE is selected, there will be no resetting of the calculations, otherwise the calculations will start from the first bar of the new period.
There is a wide range of trading strategies that make use of correlation coefficients between assets, some examples are:
Pair Trading: Traders may wish to take advantage of divergences in the price movements of highly positively correlated assets; even highly positively correlated assets do not always move in the same direction; when assets with a correlation close to +1.0 diverge in their behavior, traders may see this as an opportunity to buy one and sell the other in the expectation that the assets will return to the likely same price behavior.
Sector rotation: Traders may want to favor some sectors that are expected to perform in the next cycle, tracking the correlation between different sectors and between the sector and the overall market.
Diversification: Traders can aim to have a diversified portfolio of uncorrelated assets. From a risk management perspective, it is useful to know the correlation between the assets in your portfolio, if you hold equal positions in positively correlated assets, your risk is tilted in the same direction, so if the assets move against you, your risk is doubled. You can avoid this increased risk by choosing uncorrelated assets so that they move independently.
Hedging: Traders may want to hedge positions with correlated assets, from a hedging perspective, if you are long an asset, you can hedge going long a negative correlated asset or going short a positive correlated asset.
Traders generally need to develop awareness, a key point is to be aware of the relationships between the assets we hold or trade, the historical correlation is an invaluable tool in our arsenal which allows us to make better informed decisions.
On this chart we have an example of historical correlations for several futures markets.
We can clearly see how positively correlated the Nasdaq100 and Dow30 are with the SP500 over the whole period, or how the correlation between the Euro and the SP500 falls from almost +85% to almost -4% since 2021.
As we can see, correlations, like everything else in the market, are not static and vary over time depending on many factors, from macro to technical and everything in between.
🔹 Heatmap
The chart above shows the tool with the default settings and the Drawing Mode set to 'HEATMAP'.
We can see the current correlation between the assets, in this case the FX pairs.
The highest positive correlation is +90% (+0.90) between EURUSD and GBPUSD.
The highest negative correlation is -78% (-0.78) between EURUSD and USDJPY.
The pair with no correlation is AUDUSD and EURCAD with 1% (0.01)
On the above chart we can see the current correlations for the futures markets.
Currently, the assets that are less correlated to the SP500 are NaturalGas and the Euro, the more positive correlations are Nasdaq100 and Dow20, and the more negative correlations are the Yen, Treasury Bonds and 10-Year Notes.
🔶 DETAILS
🔹 Anchor Period
This chart shows the standard FX correlations with the Anchor Period set to `MONTHLY`.
We can clearly see how the calculations restart with the new month, in this case we can clearly see the differences between the correlations from month to month.
Let us look at the correlation coefficient between GBPUSD and USDJPY
In January, their correlation started at close to -100%, rose to close to +50%, only to fall to close to 0% and remain there for the second half of the month.
In February it was -90% in the first few days of the month and is now around -57%.
And between AUDUSD and EURCAD
Last month their correlation was negative for most of the month, reaching -70% and ending around -14%.
This month their correlation has never gone below +21% and at the time of writing is close to +53%.
🔶 SETTINGS
Anchor point: Starting point from which the tool is executed
Anchor period: At the beginning of each new period, the tool will reset the calculations
Pairs from 1 to 10: For each pair of tickers, you can: enable/disable the pair, select the color and specify the two tickers from which you wish to obtain the correlation
🔹 Style
Drawing Mode: Output style, `LINES` will show the historical correlations as lines, `HEATMAP` will show the current correlations with a color gradient from green for correlations near 1 to red for correlations near -1.
Correlation
Open Interest Inflows & Outflows [LuxAlgo]The Open Interest Inflows & Outflows indicator focuses on highlighting alterations in the overall count of active contracts associated with a specific financial instrument.
The indicator also includes an oscillator highlighting the price sentiment to use in conjunction with the open interest flow sentiment and also includes a rolling correlation of the open interest flow sentiment with a user-selected source.
🔶 USAGE
Open Interest (OI) indicates the total number of active contracts, encompassing both long and short positions, for a specific financial instrument at any given moment. This key indicator helps traders and analysts assess market activity and sentiment.
An increase in open interest generally indicates new money flowing into the market, suggesting increased activity and the potential for a trending market. Conversely, a decrease in open interest indicates that traders are closing their positions, suggesting less interest in that particular contract.
Open Interest Flow Sentiment assesses the correlation between the initiation of new positions (inflows) and the closure of existing positions (outflows) for a particular instrument. Positive values suggest a prevalence of inflows, while negative values signify a prevalence of outflows.
The magnitude of the deviation from zero reflects the extent of dominance, either in inflows or outflows.
Price Sentiment estimates the relationship between the strength of bulls (buyers) and bears (sellers) on an instrument. Positive values indicate higher bull power and negative values indicate higher bear power.
The correlation feature is a key component of the indicator and helps analyze the relationship between trading volume and Open Interest changes. If volume increases along with rising Open Interest, it supports the validity of the price trend.
A divergence between price movement, volume, and Open Interest may signal potential reversals.
🔶 DETAILS
This indicator, based on Dr. Alexander Elder's acclaimed Elder-Ray concept, aids traders in evaluating the strength of both bulls and bears by delving beneath the surface of the markets. It uncovers data not immediately apparent from a superficial glance at prices. The indicator comprises two components: Bull Power and Bear Power.
Considering that the high price of any candle signifies the maximum power of buyers and the low price represents the maximum power of sellers, Elder employs the 13-period Exponential Moving Average (EMA) to depict the average consensus of price value. Bull Power assesses whether buyers can drive prices above the average consensus of value, while Bear Power assesses whether sellers can push prices below this average.
Here are the formulas for Bull Power and Bear Power:
bull_power = high - ema(close, 13)
bear_power = low - ema(close, 13)
This concept is utilized to calculate Open Interest Flow Sentiment and Price Sentiment. The Open Interest Flow Sentiment estimates the relationship between new positions (inflows) and positions being closed (outflows), providing insights into market dynamics. The Price Sentiment, on the other hand, gauges the correlation between price movements and the Elder-Ray components, aiding traders in identifying potential shifts in market sentiment and momentum.
🔶 SETTINGS
🔹Open Interest Inflows & Outflows
OI Sentiment Correlation: toggles the visibility of Open Interest correlation with a variety of sources.
Money Flow Estimates: toggles the visibility of Money Flow Estimates calculated for the last bar.
🔹Style
OI Flow Sentiment: toggles the visibility of Open Interest Flow Sentiment, along with color customization options.
Price Sentiment: toggles the visibility of Price Sentiment, along with color customization options.
Correlation Colors: color customization option for the Correlation Area.
🔹Others
Smoothing: smoothing length applicable for Open Interest Flow Sentiment and Price Sentiment.
🔶 RELATED SCRIPTS
Open-Interest-Chart
Liquidation-Estimates
Thanks to our community for recommending this script. For more conceptual scripts and related content, we welcome you to explore by visiting >>> LuxAlgo-Scripts .
Test - Most correlated assetThis is a simple test to find the most and least correlated assets in a list.
Multi-Market Correlation Explorer [kikfraben]Multi-Market Correlation Explorer
The Multi-Market Correlation Explorer (MMCE) is a powerful tool designed to provide insights into the correlations and relative strength of various financial instruments across different markets. This indicator allows traders and investors to assess the intermarket relationships and potential opportunities by analyzing a set of ten symbols, including indices, commodities, and currencies.
Key Features:
Source Selection:
Choose your preferred data source (e.g., close, open, high, low) for all calculations.
Base Symbol for Correlations:
Define a base symbol (default: BTC/USD) for correlation calculations. The indicator evaluates how other symbols correlate with this base symbol.
Customizable Colors:
Easily identify trends with customizable colors for up and down movements, text, background, and table elements.
Length Inputs:
Tailor the analysis to your needs by adjusting the lengths for correlation calculations and RSI (Relative Strength Index).
Symbols:
Select up to ten symbols from various markets, such as stock indices, bond yields, commodities, and currencies.
Correlation Scores:
Gain insights into the strength and direction of correlations between the base symbol and selected symbols over different time lengths.
Scoring System:
Assign scores based on RSI conditions (1 for RSI > 50, -1 for RSI < 50) to each symbol.
Total Score Calculation:
Calculate a total score for each symbol by combining correlation averages and RSI scores.
Color Formatting:
Visualize correlation strengths through a color-coded system for better interpretation.
How to Use:
Positive total scores suggest potential bullish opportunities, while negative scores may indicate bearish tendencies. Combined with the visual representation of correlation strengths, traders can make informed decisions.
The Multi-Market Correlation Explorer enhances your ability to understand complex market relationships, enabling you to stay ahead of trends and identify potential trading or investment opportunities.
Sector relative strength and correlation by KaschkoThis script provides a quick overview of the relative strength and correlation of the symbols in a sector by showing a line chart of the close prices on a percent scale with all symbols starting at zero at the left side of the chart. It allows a great deal of flexibility in the configuration of the sectors and symbols in it. The standard preset sectors cover the most important futures markets and their symbols.
However, up to ten sectors with up to ten symbols each can be freely configured. Each sector is defined by a single line that has the following format:
Sector name:Symbol suffix:List of comma separated symbols
For example, the first predefined sector is defined as follows.
Energies:1!:CL,HO,NG,RB
1. The name of the sector is "Energies"
2. The suffix is "1!", i.e., to each symbol in the list "1!" is appended to get the continous future for the given symbol root. When using stock, forex or other symbols, simply leave the suffix empty.
3. The list of comma separated symbols is "CL,HO,NG,RB", i.e. crude oil, heating oil, natural gas and gasoline. As the suffix is "1!", the actual symbols whose prices are shown are "CL1!","HO1!","NG1!" and "RB1!"
You can choose to use settlement-as-close and back-adjusted contracts. The sector can also be determined automatically ("Auto-select"). In this case, it is determined to which sector the symbol currently displayed in the main chart belongs and the script displays it in the context of the other symbols in the sector.
By selecting a suitable chart time frame and time range, you can quickly determine which symbols in the sector are stronger or weaker and which are more or less strongly correlated.
The following symbols are best suited for a quick trial, as the sectors are preset for these:
CL1!,ES1!,6A1!,6B1!,6c1!,6E1!,6J1!,6M1!,6N1!,6S1!,GC1!,GF1!,HE1!,HG1!,HO1!,LBR1!,LE1!,NG1!,NQ1!,PA1!,PL1!,RB1!,SI1!,YM1!,ZB1!,ZC1!,ZF1!,ZL1!,ZM1!,ZN1!,ZO1!,ZR1!,ZS1!,ZT1!,ZW1!,CC1!,CT1!,DX1!,KC1!,OJ1!,SB1!,RTY1!
You can also use the script to compare any symbols (e.g. different shares) with each other. Preferably use the "Custom" sector for this.
Stock Data Table█ OVERVIEW
This is a table that shows some information about stocks. It is divided into four sections:
1) Correlation
2) Shares
3) Daily Data
4) Extended Session Data
The table is completely modular, which means you can add or remove each element from the settings menu, and it will automatically rearrange its spaces.
It is also highly customizable, to the extent that you can change almost any color, remove or change titles, invert section rows, and much more.
1) Correlation
The script checks if the stock is listed on NASDAQ, and if so, uses the QQQ (Nasdaq-100 ETF) as the reference index in the first cell; otherwise, it uses the SPY (S&P 500 ETF). The length of the correlation is shown in the second cell. The table then displays the correlation between the reference index and the other index, and the correlation between the reference index and the stock.
To make it easier to interpret the correlation values, each row's last cell is color-coded with a gradient to highlight the type of correlation, and the direction of the gradient can be customized.
The correlation coefficient is a statistical measure that quantifies the strength and direction of the relationship between two variables, indicating how changes in one variable are associated with changes in the other variable, so it can be used to identify patterns and trends.
If you are interested in correlation, I suggest taking a look at my dedicated indicator:
2) Shares
This feature provides you with quick access to key information about shares and market capitalization.
On one row, you can view the total shares outstanding and the market capitalization for the fiscal year or the quarterly year. The total shares outstanding represents the total number of shares of the stock that have been issued and are currently outstanding, regardless of whether they are held by insiders or public investors. The market capitalization is a widely used measure of the company's value as determined by the stock market, calculated by multiplying its current stock price with the total number of outstanding shares.
The other row shows the float, which is the number of shares of a company that are available for public trading, and the corresponding free-float market cap, calculated by multiplying the company's current stock price with the float. Because Pine Script does not allow retrieving information about quarterly year float, you can view the float and the free-float market cap of the fiscal year only. The data can be displayed at all times or only when the difference between the total shares outstanding and the float is significant enough to result in a difference between the market cap and free-float market cap.
The classification for market cap and free-float market cap is set in this way:
Mega Cap: $200 billion or more
Large Cap: between $10 billion and $200 billion
Mid Cap: between $2 billion and $10 billion
Small Cap: between $300 million and $2 billion
Micro Cap: less than $300 million
Penny Stocks: less than $5 (customizable)
Comparing the free-float market cap to the market cap can provide insights into the liquidity of a stock. In fact, if the float is relatively small compared to the total shares outstanding, it may be more difficult to find buyers or sellers, which could lead to increased volatility. On the other hand, a larger float indicates that the stock is more liquid and may be easier to trade, potentially resulting in lower volatility. However, market conditions can change quickly and significantly, especially for intraday traders, and the free-float can also change as insiders or other large shareholders buy or sell shares. Therefore, comparing the data of the fiscal year with that of the quarterly year may not provide the most up-to-date and accurate information for making trading decisions. This limitation can be mitigated by combining those data with other indicators and tools, such as technical analysis or news events, to gain a better understand of the stock's performance and potential trading opportunities.
3) Daily Data
This section is available on daily charts only due to the lack of accuracy of real-time daily data on other time frames. Here, you can view the Average Daily Volume (ADV) over a preferred time range (20 days by default), and the Daily Change, which represents the percentage difference between the closing price on two consecutive trading days.
ADV is useful in measuring the stock's volatility, as it provides an indication of how much trading activity there is in it. Generally speaking, stocks with higher trading volume tend to be less volatile than stocks with lower trading volume. High trading volume means there are more buyers and sellers actively trading the stock, which makes it easier for investors to buy and sell shares at fair prices. This increased liquidity can help to stabilize the stock price, reducing the potential for large swings in either direction. On the other hand, stocks with lower trading volume may experience greater volatility, as there are fewer buyers and sellers actively trading the stock. This can result in larger price swings, as it may be more difficult for investors to buy or sell shares at fair prices.
The daily percentage change can provide an indication of the stock's volatility, with larger values indicating greater volatility and risk. It can also be compared to that of a benchmark such an index or other stocks in the same sector, helping to determine whether the stock is outperforming or underperforming relative to them.
4) Extended Session Data
The fourth section is available on intraday charts only. This section provides two pieces of information: the Extended Session Change and the Pre-Market Volume.
The Extended Session Change indicates the percentage difference between the previous day's closing price and the latest price in the extended session. This gives you the extent and the direction of the price gap that occurred during extended trading hours.
The Pre-Market Volume shows the sum of all shares traded during the pre-market session. This can be helpful in understanding how much interest the stock gained before the market opened.
By default, the two rows will be visible at all times. They will stop updating after the end of their respective time range, and resume updating when it starts again. However, you can choose to automatically hide them outside of their time ranges.
Both the extended session and pre-market time ranges can be customized. Please note that if you select time ranges outside of the regular market session (as set by default), you must enable the extended session to view the corresponding rows.
█ GENERAL NOTES
• Total Shares Outstanding, Float, Average Daily Volume and Pre-Market Volume cells use a customizable color system based on two thresholds, to help you quickly identify whether the value is "too low/acceptable/too high" or "too low/not enough high/acceptable".
• If you cannot see certain data, that simply means it is not available.
Quantitative Risk Navigator [kikfraben]📊 Quantitative Risk Navigator - Your Financial Performance GPS
Navigate the complexities of financial markets with confidence using the Quantitative Risk Navigator. This indicator provides you with a comprehensive dashboard to assess and understand the risk and performance of your chosen asset.
📈 Key Features:
Alpha and Beta Analysis: Uncover the outperformance (Alpha) and risk exposure (Beta) of your asset compared to a selected benchmark. Know where your investment stands in the market.
Correlation Insights: Understand the relationship between your asset and its benchmark through a clear visualization of correlation trends over different time lengths.
Risk-Return Metrics: Evaluate risk and return simultaneously with Sharpe and Sortino ratios. Make informed decisions by assessing the reward-to-risk ratio of your investment.
Omega Ratio: Gain deeper insights into your asset's performance by analyzing the Omega Ratio, which highlights the distribution of positive and negative returns.
Customizable Visualization: Tailor your chart to focus on specific metrics and time frames. Choose which metrics to display, allowing you to concentrate on the aspects that matter most to you.
Interactive Metrics Table: A user-friendly metrics table provides a quick overview of key values, including average metrics, enabling you to grasp the financial health of your asset at a glance.
Color-Coded Clarity: The indicator employs color-coded visualizations, making it easy to identify bullish and bearish trends, helping you make rapid and informed decisions.
🛠️ How to Use:
Symbol Selection: Choose your base symbol and preferred data source for analysis.
Risk-Free Rate: Input your risk-free rate to fine-tune calculations.
Length Customization: Adjust the lengths for different metrics to align with your analysis preferences.
Whether you're a seasoned trader or just stepping into the financial world, the Quantitative Risk Navigator empowers you to make strategic decisions by providing a comprehensive view of your asset's risk and return profile. Stay in control of your investments with this powerful financial GPS.
🚀 Start Navigating Your Financial Journey Today!
Supertrend Multiasset Correlation - vanAmsen Hello traders!
I am elated to introduce the "Supertrend Multiasset Correlation" , a groundbreaking fusion of the trusted Supertrend with multi-asset correlation insights. This approach offers traders a nuanced, multi-layered perspective of the market.
The Underlying Concept:
Ever pondered over the term Multiasset Correlation?
In the intricate tapestry of financial markets, assets do not operate in silos. Their movements are frequently intertwined, sometimes palpably so, and at other times more covertly. Understanding these correlations can unlock deeper insights into overarching market narratives and directional trends.
By melding the Supertrend with multi-asset correlations, we craft a holistic narrative. This allows traders to fathom not merely the trend of a lone asset but to appreciate its dynamics within a broader market tableau.
Strategy Insights:
At the core of this indicator is its strategic approach. For every asset, a signal is generated based on the Supertrend parameters you've configured. Subsequently, the correlation of daily price changes is assessed. The ultimate signal on the selected asset emerges from the average of the squared correlations, factoring in their direction. This indicator not only accounts for the asset under scrutiny (hence a correlation of 1) but also integrates 12 additional assets. By default, these span U.S. growth ETFs, value ETFs, sector ETFs, bonds, and gold.
Indicator Highlights:
The "Supertrend Multiasset Correlation" isn't your run-of-the-mill Supertrend adaptation. It's a bespoke concoction, tailored to arm traders with an all-encompassing view of market intricacies, fortified with robust correlation metrics.
Key Features:
- Supertrend Line : A crystal-clear visual depiction of the prevailing market trajectory.
- Multiasset Correlation : Delve into the intricate interplay of various assets and their correlation with your primary instrument.
- Interactive Correlation Table : Nestled at the top right, this table offers a succinct overview of correlation metrics.
- Predictive Insights : Leveraging correlations to proffer predictive pointers, adding another layer of conviction to your trades.
Usage Nuances:
- The bullish Supertrend line radiates in a rejuvenating green hue, indicative of potential upward swings.
- On the flip side, the bearish trajectory stands out in a striking red, signaling possible downtrends.
- A rich suite of customization tools ensures that the chart resonates with your trading ethos.
Parting Words:
While the "Supertrend Multiasset Correlation" bestows traders with a rejuvenated perspective, it's paramount to embed it within a comprehensive trading blueprint. This would include blending it with other technical tools and adhering to stringent risk management practices. And remember, before plunging into live trades, always backtest to fine-tune your strategies.
Triple Ehlers Market StateClear trend identification is an important aspect of finding the right side to trade, another is getting the best buying/selling price on a pullback, retracement or reversal. Triple Ehlers Market State can do both.
Three is always better
Ehlers’ original formulation produces bullish, bearish and trendless signals. The indicator presented here gate stages three correlation cycles of adjustable lengths and degree thresholds, displaying a more refined view of bullish, bearish and trendless markets, in a compact and novel way.
Stick with the default settings, or experiment with the cycle period and threshold angle of each cycle, then choose whether ‘Recent trend weighting’ is included in candle colouring.
John Ehlers is a highly respected trading maths head who may need no introduction here. His idea for Market State was published in TASC June 2020 Traders Tips. The awesome interpretation of Ehlers’ work on which Triple Ehlers Market State’s correlation cycle calculations are based can be found at:
DISCLAIMER: None of this is financial advice.
K's Reversal Indicator IIIK's Reversal Indicator III is based on the concept of autocorrelation of returns. The main theory is that extreme autocorrelation (trending) that coincide with a technical signals such as one from the RSI, may result in a powerful short-term signal that can be exploited.
The indicator is calculated as follows:
1. Calculate the price differential (returns) as the current price minus the previous price.
2. the correlation between the current return and the return from 14 periods ago using a lookback of 14 periods.
3. Calculate a 14-period RSI on the close prices.
To generate the signals, use the following rules:
* A bullish signal is generated whenever the correlation is above 0.60 while the RSI is below 40.
* A bearish signal is generated whenever the correlation is above 0.60 while the RSI is above 60.
Robust Bollinger Bands with Trend StrengthThe "Robust Bollinger Bands with Trend Strength" indicator is a technical analysis tool designed assess price volatility, identify potential trading opportunities, and gauge trend strength. It combines several robust statistical methods and percentile-based calculations to provide valuable information about price movements with Improved Resilience to Noise while mitigating the impact of outliers and non-normality in price data.
Here's a breakdown of how this indicator works and the information it provides:
Bollinger Bands Calculation: Similar to traditional Bollinger Bands, this indicator calculates the upper and lower bands that envelop the median (centerline) of the price data. These bands represent the potential upper and lower boundaries of price movements.
Robust Statistics: Instead of using standard deviation, this indicator employs robust statistical measures to calculate the bands (spread). Specifically, it uses the Interquartile Range (IQR), which is the range between the 25th percentile (low price) and the 75th percentile (high price). Robust statistics are less affected by extreme values (outliers) and data distributions that may not be perfectly normal. This makes the bands more resistant to unusual price spikes.
Median as Centerline: The indicator utilizes the median of the chosen price source (either HLC3 or VWMA) as the central reference point for the bands. The median is less affected by outliers than the mean (average), making it a robust choice. This can help identify the center of price action, which is useful for understanding whether prices are trending or ranging.
Trend Strength Assessment: The indicator goes beyond the standard Bollinger Bands by incorporating a measure of trend strength. It uses a robust rank-based correlation coefficient to assess the relationship between the price source and the bar index (time). This correlation coefficient, calculated over a specified length, helps determine whether a trend is strong, positive (uptrend), negative (down trend), or non-existent and weak. When the rank-based correlation coefficient shifts it indicates exhaustion of a prevailing trend. Trend Strength" indicator is designed to provide statistically valid information about trend strength while minimizing the impact of outliers and data distribution characteristics. The parameter choices, including a length of 14 and a correlation threshold of +/-0.7, considered to offer meaningful insights into market conditions and statistical validity (p-value ,0.05 statistically significant). The use of rank-based correlation is a robust alternative to traditional Pearson correlation, especially in the context of financial markets.
Trend Fill: Based on the robust rank-based correlation coefficient, the indicator fills the area between the upper and lower Bollinger Bands with different colors to visually represent the trend strength. For example, it may use green for an uptrend, red for a down trend, and a neutral color for a weak or ranging market. This visual representation can help traders quickly identify potential trend opportunities. In addition the middle line also informs about the overall trend direction of the median.
Cross Correlation [Kioseff Trading]Hello!
This script "Cross Correlation" calculates up to ~10,000 lag-symbol pair cross correlation values simultaneously!
Cross correlation calculation for 20 symbols simultaneously
+/- Lag Range is theoretically infinite (configurable min/max)
Practically, calculate up to 10000 lag-symbol pairs
Results can be sorted by greatest absolute difference or greatest sum
Ability to "isolate" the symbol on your chart and check for cross correlation against a list of symbols
Script defaults to stock pairs when on a stock, Forex pairs when on a Forex pair, crypto when on a crypto coin, futures when on a futures contract.
A custom symbol list can be used for cross correlation checking
Can check any number of available historical data points for cross correlation
Practical Assessment
Ideally, we can calculate cross correlation to determine if, in a list of assets, any of the assets frequently lead or lag one another.
Example
Say we are comparing the log returns for the previous 10 days for SPY and XLU.
*A single time-interval corresponds to the timeframe of your chart i.e. 1-minute chart = 1-minute time interval. We're using days for this example.
(Example Results)
A lag value (k) +/-3 is used.
The cross correlation (normalized) for k = +3 is -0.787
The cross correlation (normalized) for k = -3 is 0.216
A positive "k" value indicates the correlation when Asset A (SPY) leads Asset B (XLU)
A negative "k" value indicates the correlation when Asset B (XLU) leads Asset A (SPY)
A normalized cross correlation of -0.787 for k = +3 indicates an "adequately strong" negative relationship when SPY leads XLU by 3 days.
When SPY increases or decreases - XLU frequently moves in the opposite direction 3 days later.
A cross correlation value of 0.216 at k = −3 indicates a "weak" positive correlation when XLU leads SPY by 3 days.
There's a slight tendency for SPY to move in the same direction as XLU 3 days later.
After the cross-correlation score is normalized it will fall between -1 and 1.
A cross-correlation score of 1 indicates a perfect directional relationship between asset A and asset B at the corresponding lag (k).
A cross correlation of -1 indicates a perfect inverse relationship between asset A and asset B at the corresponding lag (k).
A cross correlation of 0 indicates no correlation at the corresponding lag (k).
The image above shows the primary usage for the script!
The image above further explains the data points located in the table!
The image above shows the script "isolating" the symbol on my chart and checking the cross correlation between the symbol and a list of symbols!
Wrapping Up
With this information, hopefully you can find some meaningful lead-lag relationships amongst assets!
Thank you for checking this out (:
Multi-Asset Performance [Spaghetti] - By LeviathanThis indicator visualizes the cumulative percentage changes or returns of 30 symbols over a given period and offers a unique set of tools and data analytics for deeper insight into the performance of different assets.
Multi Asset Performance indicator (also called “Spaghetti”) makes it easy to monitor the changes in Price, Open Interest, and On Balance Volume across multiple assets simultaneously, distinguish assets that are overperforming or underperforming, observe the relative strength of different assets or currencies, use it as a tool for identifying mean reversion opportunities and even for constructing pairs trading strategies, detect "risk-on" or "risk-off" periods, evaluate statistical relationships between assets through metrics like correlation and beta, construct hedging strategies, trade rotations and much more.
Start by selecting a time period (e.g., 1 DAY) to set the interval for when data is reset. This will provide insight into how price, open interest, and on-balance volume change over your chosen period. In the settings, asset selection is fully customizable, allowing you to create three groups of up to 30 tickers each. These tickers can be displayed in a variety of styles and colors. Additional script settings offer a range of options, including smoothing values with a Simple Moving Average (SMA), highlighting the top or bottom performers, plotting the group mean, applying heatmap/gradient coloring, generating a table with calculations like beta, correlation, and RSI, creating a profile to show asset distribution around the mean, and much more.
One of the most important script tools is the screener table, which can display:
🔸 Percentage Change (Represents the return or the percentage increase or decrease in Price/OI/OBV over the current selected period)
🔸 Beta (Represents the sensitivity or responsiveness of asset's returns to the returns of a benchmark/mean. A beta of 1 means the asset moves in tandem with the market. A beta greater than 1 indicates the asset is more volatile than the market, while a beta less than 1 indicates the asset is less volatile. For example, a beta of 1.5 means the asset typically moves 150% as much as the benchmark. If the benchmark goes up 1%, the asset is expected to go up 1.5%, and vice versa.)
🔸 Correlation (Describes the strength and direction of a linear relationship between the asset and the mean. Correlation coefficients range from -1 to +1. A correlation of +1 means that two variables are perfectly positively correlated; as one goes up, the other will go up in exact proportion. A correlation of -1 means they are perfectly negatively correlated; as one goes up, the other will go down in exact proportion. A correlation of 0 means that there is no linear relationship between the variables. For example, a correlation of 0.5 between Asset A and Asset B would suggest that when Asset A moves, Asset B tends to move in the same direction, but not perfectly in tandem.)
🔸 RSI (Measures the speed and change of price movements and is used to identify overbought or oversold conditions of each asset. The RSI ranges from 0 to 100 and is typically used with a time period of 14. Generally, an RSI above 70 indicates that an asset may be overbought, while RSI below 30 signals that an asset may be oversold.)
⚙️ Settings Overview:
◽️ Period
Periodic inputs (e.g. daily, monthly, etc.) determine when the values are reset to zero and begin accumulating again until the period is over. This visualizes the net change in the data over each period. The input "Visible Range" is auto-adjustable as it starts the accumulation at the leftmost bar on your chart, displaying the net change in your chart's visible range. There's also the "Timestamp" option, which allows you to select a specific point in time from where the values are accumulated. The timestamp anchor can be dragged to a desired bar via Tradingview's interactive option. Timestamp is particularly useful when looking for outperformers/underperformers after a market-wide move. The input positioned next to the period selection determines the timeframe on which the data is based. It's best to leave it at default (Chart Timeframe) unless you want to check the higher timeframe structure of the data.
◽️ Data
The first input in this section determines the data that will be displayed. You can choose between Price, OI, and OBV. The second input lets you select which one out of the three asset groups should be displayed. The symbols in the asset group can be modified in the bottom section of the indicator settings.
◽️ Appearance
You can choose to plot the data in the form of lines, circles, areas, and columns. The colors can be selected by choosing one of the six pre-prepared color palettes.
◽️ Labeling
This input allows you to show/hide the labels and select their appearance and size. You can choose between Label (colored pointed label), Label and Line (colored pointed label with a line that connects it to the plot), or Text Label (colored text).
◽️ Smoothing
If selected, this option will smooth the values using a Simple Moving Average (SMA) with a custom length. This is used to reduce noise and improve the visibility of plotted data.
◽️ Highlight
If selected, this option will highlight the top and bottom N (custom number) plots, while shading the others. This makes the symbols with extreme values stand out from the rest.
◽️ Group Mean
This input allows you to select the data that will be considered as the group mean. You can choose between Group Average (the average value of all assets in the group) or First Ticker (the value of the ticker that is positioned first on the group's list). The mean is then used in calculations such as correlation (as the second variable) and beta (as a benchmark). You can also choose to plot the mean by clicking on the checkbox.
◽️ Profile
If selected, the script will generate a vertical volume profile-like display with 10 zones/nodes, visualizing the distribution of assets below and above the mean. This makes it easy to see how many or what percentage of assets are outperforming or underperforming the mean.
◽️ Gradient
If selected, this option will color the plots with a gradient based on the proximity of the value to the upper extreme, zero, and lower extreme.
◽️ Table
This section includes several settings for the table's appearance and the data displayed in it. The "Reference Length" input determines the number of bars back that are used for calculating correlation and beta, while "RSI Length" determines the length used for calculating the Relative Strength Index. You can choose the data that should be displayed in the table by using the checkboxes.
◽️ Asset Groups
This section allows you to modify the symbols that have been selected to be a part of the 3 asset groups. If you want to change a symbol, you can simply click on the field and type the ticker of another one. You can also show/hide a specific asset by using the checkbox next to the field.
Advanced Weighted Residual Arbitrage AnalyzerThe Advanced Weighted Residual Arbitrage Analyzer is a sophisticated tool designed for traders aiming to exploit price deviations between various asset pairs. By examining the differences in normalized price relations and their weighted residuals, this indicator provides insights into potential arbitrage opportunities in the market.
Key Features:
Multiple Relation Analysis: Analyze up to five different asset relations simultaneously, offering a comprehensive view of potential arbitrage setups.
Normalization Functions: Choose from a variety of normalization techniques like SMA, EMA, WMA, and HMA to ensure accurate comparisons between different price series.
Dynamic Weighting: Residuals are weighted based on their correlation, ensuring that stronger correlations have a more pronounced impact on the analysis. Weighting can be adjusted using several functions including square, sigmoid, and logistic.
Regression Flexibility: Incorporate linear, polynomial, or robust regression to calculate residuals, tailoring the analysis to different market conditions.
Customizable Display: Decide which plots to display for clarity and focus, including normalized relations, weighted residuals, and the difference between the screen relation and the average weighted residual.
Usage Guidelines:
Configure the asset pairs you wish to analyze using the Symbol Relations group in the settings.
Adjust the normalization, volatility, regression, and weighting functions based on your preference and the specific characteristics of the asset pairs.
Monitor the weighted residuals for deviations from the mean. Larger deviations suggest stronger arbitrage opportunities.
Use the difference plot (between the screen relation and average weighted residual) as a quick visual cue for potential trade setups. When this plot deviates significantly from zero, it indicates a possible arbitrage opportunity.
Regularly update and adjust the parameters to account for changing market conditions and ensure the most accurate analysis.
In the Advanced Weighted Residual Arbitrage Analyzer , the value set in Alert Threshold plays a crucial role in delineating a normalized band. This band serves as a guide to identify significant deviations and potential trading opportunities.
When we observe the plots of the green line and the purple line, the Alert Threshold provides a boundary for these plots. The following points explain the significance:
Breach of the Band: When either the green or purple line crosses above or below the Alert Threshold , it indicates a significant deviation from the mean. This breach can be interpreted as a potential trading signal, suggesting a possible arbitrage opportunity.
Convergence to the Mean: If the green line converges with the purple line , it denotes that the price relation has reverted to its mean. This convergence typically suggests that the arbitrage opportunity has been exhausted, and the market dynamics are returning to equilibrium.
Trade Execution: A trader can consider entering a trade when the lines breach the Alert Threshold . The return of the green line to align closely with the purple line can be seen as a signal to exit the trade, capitalizing on the reversion to the mean.
By monitoring these plots in conjunction with the Alert Threshold , traders can gain insights into market imbalances and exploit potential arbitrage opportunities. The convergence and divergence of these lines, relative to the normalized band, serve as valuable visual cues for trade initiation and termination.
When you're analyzing relations between two symbols (for instance, BINANCE:SANDUSDT/BINANCE:NEARUSDT ), you're essentially looking at the price relationship between the two underlying assets. This relationship provides insights into potential imbalances between the assets, which arbitrage traders can exploit.
Breach of the Lower Band: If the purple line touches or crosses below the lower Alert Threshold , it indicates that the first symbol (in our example, SANDUSDT ) is undervalued relative to the second symbol ( NEARUSDT ). In practical terms:
Action: You would consider buying the first symbol ( SANDUSDT ) and selling the second symbol ( NEARUSDT ).
Rationale: The expectation is that the price of the first symbol will rise, or the price of the second symbol will fall, or both, thereby converging back to their historical mean relationship.
Breach of the Upper Band: Conversely, if the difference plot touches or crosses above the upper Alert Threshold , it suggests that the first symbol is overvalued compared to the second. This implies:
Action: You'd consider selling the first symbol ( SANDUSDT ) and buying the second symbol ( NEARUSDT ).
Rationale: The anticipation here is that the price of the first symbol will decrease, or the price of the second will increase, or both, bringing the relationship back to its historical average.
Convergence to the Mean: As mentioned earlier, when the green line aligns closely with the purple line, it's an indication that the assets have returned to their typical price relationship. This serves as a signal for traders to consider closing out their positions, locking in the gains from the arbitrage opportunity.
It's important to note that when you're trading based on symbol relations, you're essentially betting on the relative performance of the two assets. This strategy, often referred to as "pairs trading," seeks to capitalize on price imbalances between related financial instruments. By taking opposing positions in the two symbols, traders aim to profit from the eventual reversion of the price difference to the mean.
Price and Indicator CorrelationFIRST, CHANGE SOURCE OF INDICATOR FROM CLOSE TO WHATEVER INDICATOR YOU ARE COMPARING TO PRICE!!!!
Confirming Indicator Validity: By calculating the correlation coefficient between the price and a specific indicator, you can assess the degree to which the indicator and price move together. If there is a high positive correlation, it suggests that the indicator tends to move in the same direction as the price, increasing confidence in the indicator's validity. On the other hand, a low or negative correlation may indicate a weaker relationship between the indicator and price, signaling caution in relying solely on that indicator for trading decisions.
Identifying Divergence: Divergence occurs when the price and the indicator move in opposite directions. By monitoring the correlation coefficient, you can identify periods of divergence between the price and the selected indicator. Divergence may signal a potential reversal or significant price move, providing an opportunity to enter or exit trades.
Enhancing Trading Strategies: The correlation coefficient can be used to enhance trading strategies by incorporating the relationship between the price and the indicator. For example, if the correlation coefficient consistently shows a strong positive correlation, you may use the indicator as a confirmation tool for price-based trading signals. Conversely, if the correlation is consistently negative, it may indicate an inverse relationship that could be used for contrarian trading strategies.
Indicator Optimization : The correlation coefficient can help traders compare the effectiveness of different indicators. By calculating the correlation coefficient for multiple indicators against the price, you can identify which indicators have a stronger or weaker relationship with price movements. This information can guide the selection and optimization of indicators in your trading strategy.
Example:
Correlation for Major Markets This indicator plots the correlation of major markets as an indicator. The major markets covered are the following:
DXY
GC
CL
ES
RTY
ZN
The chart shows all the correlations and cross-correlations of the above instruments plotted together. The user can go in the settings and choose what correlation to see, or if multiple correlations, choose to plot the indicator a second time.
Linear Correlation Coefficient W/ MAs and Significance TestsThis Linear CC takes into account the log-normal distribution of stock prices and performs Pearson correlation on that data set. It also smoothens the results into an easy to read oscillator, and performs a two-tail t-test on the correlation coefficient data (with a = 0.05) to determine the significance of the coefficients. Significant results are shown in a solid yellow color while insignificant results are shown in a dark yellow color (you can eyeball this with a normal LCC by looking at results around -0.5 to +0.5).
Two MAs are provided as well for a quick trend analysis. You can reduce the lookback period, but it defaults to 31 for the sake of statistical standards.
Correlation TrackerCorrelation Tracker Indicator
The Correlation Tracker indicator calculates and visualizes the correlation between two symbols on a chart. It helps traders and investors understand the relationship and strength of correlation between the selected symbol and another symbol of their choice.
Indicator Features:
- Correlation Calculation: The indicator calculates the correlation between two symbols based on the provided lookback period.
- Correlation Scale: The correlation value is normalized to a scale ranging from 0 to 1 for easy interpretation.
- Table Display: A table is displayed on the chart showing the correlation value and a descriptive label indicating the strength of the correlation.
- Customization Options: Users can customize the text color, table background color, and choose whether to display the Pearson correlation value.
- The Correlation Tracker indicator utilizes a logarithmic scale calculation, making it particularly suitable for longer timeframes such as weekly charts, thereby providing a more accurate and balanced measure of correlations across a wide range of values.
How to Use:
1. Select the symbol for which you want to track the correlation (default symbol is "SPX").
2. Adjust the lookback period to define the historical data range for correlation calculation.
3. Customize the text color and table background color according to your preference.
4. Choose whether to display the Pearson correlation value or a descriptive label for correlation strength.
5. Observe the correlation line on the chart, which changes color based on the strength of the correlation.
6. Refer to the correlation table for the exact correlation value or the descriptive label indicating the correlation strength.
Note: The indicator can be applied to any time frame chart and is not limited to logarithmic scale.
Source CorrelationIn this small indicator I make it possible for the user to set two different input sources. Then, the indicator displays the correlation of these two input sources. It's a very small script, but I think it could be helpful to somebody to find uncorrelated indicators for his trading strategy. To use uncorrelated indicators is in general recommended.
Enjoy this small, but powerful tool. 🧙♂️
Correlation Coefficient - DXY & XAUPublishing my first indicator on TradingView. Essentially a modification of the Correlation Coefficient indicator, that displays a 2 ticker symbols' correlation coefficient vs, the chart presently loaded.. You can modify the symbols, but the default uses DXY and XAU, which have been displaying strong negative correlation.
As with the built-in CC (Correlation Coefficient) indicator, readings are taken the same way:
Positive Correlation = anything above 0 | stronger as it moves up towards 1 | weaker as it moves back down towards 0
Negative Correlation = anything below 0 | stronger moving down towards -1 | weaker moving back up towards 0
This is primarily created to work with the Bitcoin weekly chart, for comparing DXY and Gold (XAU) price correlations (in advance, when possible). If you change the chart timeframe to something other than weekly, consider playing with the Length input, which is set to 35 by default where I think it best represents correlations with Bitcoin's weekly timeframe for DXY and Gold.
The intention is that you might be able to determine future direction of Bitcoin based on positive or negative correlations of Gold and/or the US Dollar Index. DXY has been making peaks and valleys prior to Bitcoin since after March 2020 black swan event, where it peaked just after instead. In the future, it may flip over again and Bitcoin may hit major highs or lows prior to DXY, again. So, keep an eye on the charts for all 3, as well as the indicator correlations.
Currently, we've moved back into negative correlation between Bitcoin and DXY, and positive correlation with Bitcoin and Gold:
Negative Correlation b/w Bitcoin and DXY - if DXY moves up, Bitcoin likely moves down, or if DXY moves down, Bitcoin likely moves up (or if Bitcoin were to move first before DXY, as it did on March 2020, instead)
Positive Correlation b/w Bitcoin and Gold - Bitcoin and Gold will likely move up or down with each other.
DXY is represented by the green histogram and label, Gold is represented by the yellow histogram and label. Again, you can modify the tickers you want to check against, and you can modify the colors for their histograms / labels.
The inspiration from came from noticing areas of same date or delayed negative correlation between Bitcoin and DXY, here is one of my most recent posts about that:
Please let me know if you have any questions, or would like to see updates to the indicator to make it easier to use or add more useful features to it.
I hope this becomes useful to you in some way. Thank you for your support!
Cheers,
dudebruhwhoa :)
MA Correlation CoefficientThis script helps you visualize the correlation between the price of an asset and 4 moving averages of your choice. This indicator can help you identify trendy markets as well as trend-shifts.
Disclaimer
Bear in mind that there is always some lag when using Moving-Averages, hence the purpose of this indicator is as a trend identification tool rather than an entry-exit strategy.
Working Principle
The basic idea behind this indicator is the following:
In a trendy market you will find high correlation between price and all kinds of Moving-Averages. This works both ways, no matter bull or bear trend.
In sideways markets you might find a mix of correlations accross timeframes (2018) or high correlation with Low-Timeframe averages and low correlation with High-Timeframe averages (2021/2022).
Trend shifts might be characterised by a 'staircase' type of correlation (yellow), where the asset regains correlation with higher timeframe averages
Indicator Options
1. Source : data used for indicator calculation
1. Correlation Window : size of moving window for correlation calculation
2. Average Type :
Simple-Moving-Average (SMA)
Exponential-Moving-Average (EMA)
Hull-Moving-Average (HMA)
Volume-Weighted-Moving-Average (VWMA)
3. Lookback : number of past candles to calculate average
4. Gradient : modify gradient colors. colors relate to correlation values.
Plot Explanation
The indicator plots, using colors, the correlation of the asset with 4 averages. For every candle, 4 correlation values are generated, corresponding to 4 colors. These 4 colors are stacked one on top of the other generating the patterns explained above. These patterns may help you identify what kind of market you're in.
Crypto Correlation MatrixA crypto correlation matrix or table is a tool that displays the correlation between different cryptocurrencies and other financial assets. The matrix provides an overview of the degree to which various cryptocurrencies move in tandem or independently of each other. Each cell represents the correlation between the row and column assets respectively.
The correlation matrix can be useful for traders and investors in several ways:
First, it allows them to identify trends and patterns in the behavior of different cryptocurrencies. By looking at the correlations between different assets, traders can gain insight into the intra-relationships of the crypto market and make more informed trading decisions. For example, if two cryptocurrencies have a high positive correlation, meaning that they tend to move in the same direction, a trader may want to diversify their portfolio by choosing to invest in only one of the two assets.
Additionally, the correlation matrix can help traders and investors to manage risk. By analyzing the correlations between different assets, traders can identify opportunities to hedge their positions or limit their exposure to particular risks. For example, if a trader holds a portfolio of cryptocurrencies that are highly correlated with each other, they may be at greater risk of losses if the market moves against them. By diversifying their portfolio with assets that are less correlated with each other, they can reduce their overall risk.
Some of the unique properties for this specific script are the correlation strength levels in conjunction with the color gradient of cells, intended for clearer readability.
Features:
Supports up to 64 different crypto assets.
Dark/Light mode.
Correlation strength levels and cell coloring.
Adjustable positioning on the chart.
Alerts at the close of a bar. (Daily timeframe or higher recommended)
loxxfftLibrary "loxxfft"
This code is a library for performing Fast Fourier Transform (FFT) operations. FFT is an algorithm that can quickly compute the discrete Fourier transform (DFT) of a sequence. The library includes functions for performing FFTs on both real and complex data. It also includes functions for fast correlation and convolution, which are operations that can be performed efficiently using FFTs. Additionally, the library includes functions for fast sine and cosine transforms.
Reference:
www.alglib.net
fastfouriertransform(a, nn, inversefft)
Returns Fast Fourier Transform
Parameters:
a (float ) : float , An array of real and imaginary parts of the function values. The real part is stored at even indices, and the imaginary part is stored at odd indices.
nn (int) : int, The number of function values. It must be a power of two, but the algorithm does not validate this.
inversefft (bool) : bool, A boolean value that indicates the direction of the transformation. If True, it performs the inverse FFT; if False, it performs the direct FFT.
Returns: float , Modifies the input array a in-place, which means that the transformed data (the FFT result for direct transformation or the inverse FFT result for inverse transformation) will be stored in the same array a after the function execution. The transformed data will have real and imaginary parts interleaved, with the real parts at even indices and the imaginary parts at odd indices.
realfastfouriertransform(a, tnn, inversefft)
Returns Real Fast Fourier Transform
Parameters:
a (float ) : float , A float array containing the real-valued function samples.
tnn (int) : int, The number of function values (must be a power of 2, but the algorithm does not validate this condition).
inversefft (bool) : bool, A boolean flag that indicates the direction of the transformation (True for inverse, False for direct).
Returns: float , Modifies the input array a in-place, meaning that the transformed data (the FFT result for direct transformation or the inverse FFT result for inverse transformation) will be stored in the same array a after the function execution.
fastsinetransform(a, tnn, inversefst)
Returns Fast Discrete Sine Conversion
Parameters:
a (float ) : float , An array of real numbers representing the function values.
tnn (int) : int, Number of function values (must be a power of two, but the code doesn't validate this).
inversefst (bool) : bool, A boolean flag indicating the direction of the transformation. If True, it performs the inverse FST, and if False, it performs the direct FST.
Returns: float , The output is the transformed array 'a', which will contain the result of the transformation.
fastcosinetransform(a, tnn, inversefct)
Returns Fast Discrete Cosine Transform
Parameters:
a (float ) : float , This is a floating-point array representing the sequence of values (time-domain) that you want to transform. The function will perform the Fast Cosine Transform (FCT) or the inverse FCT on this input array, depending on the value of the inversefct parameter. The transformed result will also be stored in this same array, which means the function modifies the input array in-place.
tnn (int) : int, This is an integer value representing the number of data points in the input array a. It is used to determine the size of the input array and control the loops in the algorithm. Note that the size of the input array should be a power of 2 for the Fast Cosine Transform algorithm to work correctly.
inversefct (bool) : bool, This is a boolean value that controls whether the function performs the regular Fast Cosine Transform or the inverse FCT. If inversefct is set to true, the function will perform the inverse FCT, and if set to false, the regular FCT will be performed. The inverse FCT can be used to transform data back into its original form (time-domain) after the regular FCT has been applied.
Returns: float , The resulting transformed array is stored in the input array a. This means that the function modifies the input array in-place and does not return a new array.
fastconvolution(signal, signallen, response, negativelen, positivelen)
Convolution using FFT
Parameters:
signal (float ) : float , This is an array of real numbers representing the input signal that will be convolved with the response function. The elements are numbered from 0 to SignalLen-1.
signallen (int) : int, This is an integer representing the length of the input signal array. It specifies the number of elements in the signal array.
response (float ) : float , This is an array of real numbers representing the response function used for convolution. The response function consists of two parts: one corresponding to positive argument values and the other to negative argument values. Array elements with numbers from 0 to NegativeLen match the response values at points from -NegativeLen to 0, respectively. Array elements with numbers from NegativeLen+1 to NegativeLen+PositiveLen correspond to the response values in points from 1 to PositiveLen, respectively.
negativelen (int) : int, This is an integer representing the "negative length" of the response function. It indicates the number of elements in the response function array that correspond to negative argument values. Outside the range , the response function is considered zero.
positivelen (int) : int, This is an integer representing the "positive length" of the response function. It indicates the number of elements in the response function array that correspond to positive argument values. Similar to negativelen, outside the range , the response function is considered zero.
Returns: float , The resulting convolved values are stored back in the input signal array.
fastcorrelation(signal, signallen, pattern, patternlen)
Returns Correlation using FFT
Parameters:
signal (float ) : float ,This is an array of real numbers representing the signal to be correlated with the pattern. The elements are numbered from 0 to SignalLen-1.
signallen (int) : int, This is an integer representing the length of the input signal array.
pattern (float ) : float , This is an array of real numbers representing the pattern to be correlated with the signal. The elements are numbered from 0 to PatternLen-1.
patternlen (int) : int, This is an integer representing the length of the pattern array.
Returns: float , The signal array containing the correlation values at points from 0 to SignalLen-1.
tworealffts(a1, a2, a, b, tn)
Returns Fast Fourier Transform of Two Real Functions
Parameters:
a1 (float ) : float , An array of real numbers, representing the values of the first function.
a2 (float ) : float , An array of real numbers, representing the values of the second function.
a (float ) : float , An output array to store the Fourier transform of the first function.
b (float ) : float , An output array to store the Fourier transform of the second function.
tn (int) : float , An integer representing the number of function values. It must be a power of two, but the algorithm doesn't validate this condition.
Returns: float , The a and b arrays will contain the Fourier transform of the first and second functions, respectively. Note that the function overwrites the input arrays a and b.
█ Detailed explaination of each function
Fast Fourier Transform
The fastfouriertransform() function takes three input parameters:
1. a: An array of real and imaginary parts of the function values. The real part is stored at even indices, and the imaginary part is stored at odd indices.
2. nn: The number of function values. It must be a power of two, but the algorithm does not validate this.
3. inversefft: A boolean value that indicates the direction of the transformation. If True, it performs the inverse FFT; if False, it performs the direct FFT.
The function performs the FFT using the Cooley-Tukey algorithm, which is an efficient algorithm for computing the discrete Fourier transform (DFT) and its inverse. The Cooley-Tukey algorithm recursively breaks down the DFT of a sequence into smaller DFTs of subsequences, leading to a significant reduction in computational complexity. The algorithm's time complexity is O(n log n), where n is the number of samples.
The fastfouriertransform() function first initializes variables and determines the direction of the transformation based on the inversefft parameter. If inversefft is True, the isign variable is set to -1; otherwise, it is set to 1.
Next, the function performs the bit-reversal operation. This is a necessary step before calculating the FFT, as it rearranges the input data in a specific order required by the Cooley-Tukey algorithm. The bit-reversal is performed using a loop that iterates through the nn samples, swapping the data elements according to their bit-reversed index.
After the bit-reversal operation, the function iteratively computes the FFT using the Cooley-Tukey algorithm. It performs calculations in a loop that goes through different stages, doubling the size of the sub-FFT at each stage. Within each stage, the Cooley-Tukey algorithm calculates the butterfly operations, which are mathematical operations that combine the results of smaller DFTs into the final DFT. The butterfly operations involve complex number multiplication and addition, updating the input array a with the computed values.
The loop also calculates the twiddle factors, which are complex exponential factors used in the butterfly operations. The twiddle factors are calculated using trigonometric functions, such as sine and cosine, based on the angle theta. The variables wpr, wpi, wr, and wi are used to store intermediate values of the twiddle factors, which are updated in each iteration of the loop.
Finally, if the inversefft parameter is True, the function divides the result by the number of samples nn to obtain the correct inverse FFT result. This normalization step is performed using a loop that iterates through the array a and divides each element by nn.
In summary, the fastfouriertransform() function is an implementation of the Cooley-Tukey FFT algorithm, which is an efficient algorithm for computing the DFT and its inverse. This FFT library can be used for a variety of applications, such as signal processing, image processing, audio processing, and more.
Feal Fast Fourier Transform
The realfastfouriertransform() function performs a fast Fourier transform (FFT) specifically for real-valued functions. The FFT is an efficient algorithm used to compute the discrete Fourier transform (DFT) and its inverse, which are fundamental tools in signal processing, image processing, and other related fields.
This function takes three input parameters:
1. a - A float array containing the real-valued function samples.
2. tnn - The number of function values (must be a power of 2, but the algorithm does not validate this condition).
3. inversefft - A boolean flag that indicates the direction of the transformation (True for inverse, False for direct).
The function modifies the input array a in-place, meaning that the transformed data (the FFT result for direct transformation or the inverse FFT result for inverse transformation) will be stored in the same array a after the function execution.
The algorithm uses a combination of complex-to-complex FFT and additional transformations specific to real-valued data to optimize the computation. It takes into account the symmetry properties of the real-valued input data to reduce the computational complexity.
Here's a detailed walkthrough of the algorithm:
1. Depending on the inversefft flag, the initial values for ttheta, c1, and c2 are determined. These values are used for the initial data preprocessing and post-processing steps specific to the real-valued FFT.
2. The preprocessing step computes the initial real and imaginary parts of the data using a combination of sine and cosine terms with the input data. This step effectively converts the real-valued input data into complex-valued data suitable for the complex-to-complex FFT.
3. The complex-to-complex FFT is then performed on the preprocessed complex data. This involves bit-reversal reordering, followed by the Cooley-Tukey radix-2 decimation-in-time algorithm. This part of the code is similar to the fastfouriertransform() function you provided earlier.
4. After the complex-to-complex FFT, a post-processing step is performed to obtain the final real-valued output data. This involves updating the real and imaginary parts of the transformed data using sine and cosine terms, as well as the values c1 and c2.
5. Finally, if the inversefft flag is True, the output data is divided by the number of samples (nn) to obtain the inverse DFT.
The function does not return a value explicitly. Instead, the transformed data is stored in the input array a. After the function execution, you can access the transformed data in the a array, which will have the real part at even indices and the imaginary part at odd indices.
Fast Sine Transform
This code defines a function called fastsinetransform that performs a Fast Discrete Sine Transform (FST) on an array of real numbers. The function takes three input parameters:
1. a (float array): An array of real numbers representing the function values.
2. tnn (int): Number of function values (must be a power of two, but the code doesn't validate this).
3. inversefst (bool): A boolean flag indicating the direction of the transformation. If True, it performs the inverse FST, and if False, it performs the direct FST.
The output is the transformed array 'a', which will contain the result of the transformation.
The code starts by initializing several variables, including trigonometric constants for the sine transform. It then sets the first value of the array 'a' to 0 and calculates the initial values of 'y1' and 'y2', which are used to update the input array 'a' in the following loop.
The first loop (with index 'jx') iterates from 2 to (tm + 1), where 'tm' is half of the number of input samples 'tnn'. This loop is responsible for calculating the initial sine transform of the input data.
The second loop (with index 'ii') is a bit-reversal loop. It reorders the elements in the array 'a' based on the bit-reversed indices of the original order.
The third loop (with index 'ii') iterates while 'n' is greater than 'mmax', which starts at 2 and doubles each iteration. This loop performs the actual Fast Discrete Sine Transform. It calculates the sine transform using the Danielson-Lanczos lemma, which is a divide-and-conquer strategy for calculating Discrete Fourier Transforms (DFTs) efficiently.
The fourth loop (with index 'ix') is responsible for the final phase adjustments needed for the sine transform, updating the array 'a' accordingly.
The fifth loop (with index 'jj') updates the array 'a' one more time by dividing each element by 2 and calculating the sum of the even-indexed elements.
Finally, if the 'inversefst' flag is True, the code scales the transformed data by a factor of 2/tnn to get the inverse Fast Sine Transform.
In summary, the code performs a Fast Discrete Sine Transform on an input array of real numbers, either in the direct or inverse direction, and returns the transformed array. The algorithm is based on the Danielson-Lanczos lemma and uses a divide-and-conquer strategy for efficient computation.
Fast Cosine Transform
This code defines a function called fastcosinetransform that takes three parameters: a floating-point array a, an integer tnn, and a boolean inversefct. The function calculates the Fast Cosine Transform (FCT) or the inverse FCT of the input array, depending on the value of the inversefct parameter.
The Fast Cosine Transform is an algorithm that converts a sequence of values (time-domain) into a frequency domain representation. It is closely related to the Fast Fourier Transform (FFT) and can be used in various applications, such as signal processing and image compression.
Here's a detailed explanation of the code:
1. The function starts by initializing a number of variables, including counters, intermediate values, and constants.
2. The initial steps of the algorithm are performed. This includes calculating some trigonometric values and updating the input array a with the help of intermediate variables.
3. The code then enters a loop (from jx = 2 to tnn / 2). Within this loop, the algorithm computes and updates the elements of the input array a.
4. After the loop, the function prepares some variables for the next stage of the algorithm.
5. The next part of the algorithm is a series of nested loops that perform the bit-reversal permutation and apply the FCT to the input array a.
6. The code then calculates some additional trigonometric values, which are used in the next loop.
7. The following loop (from ix = 2 to tnn / 4 + 1) computes and updates the elements of the input array a using the previously calculated trigonometric values.
8. The input array a is further updated with the final calculations.
9. In the last loop (from j = 4 to tnn), the algorithm computes and updates the sum of elements in the input array a.
10. Finally, if the inversefct parameter is set to true, the function scales the input array a to obtain the inverse FCT.
The resulting transformed array is stored in the input array a. This means that the function modifies the input array in-place and does not return a new array.
Fast Convolution
This code defines a function called fastconvolution that performs the convolution of a given signal with a response function using the Fast Fourier Transform (FFT) technique. Convolution is a mathematical operation used in signal processing to combine two signals, producing a third signal representing how the shape of one signal is modified by the other.
The fastconvolution function takes the following input parameters:
1. float signal: This is an array of real numbers representing the input signal that will be convolved with the response function. The elements are numbered from 0 to SignalLen-1.
2. int signallen: This is an integer representing the length of the input signal array. It specifies the number of elements in the signal array.
3. float response: This is an array of real numbers representing the response function used for convolution. The response function consists of two parts: one corresponding to positive argument values and the other to negative argument values. Array elements with numbers from 0 to NegativeLen match the response values at points from -NegativeLen to 0, respectively. Array elements with numbers from NegativeLen+1 to NegativeLen+PositiveLen correspond to the response values in points from 1 to PositiveLen, respectively.
4. int negativelen: This is an integer representing the "negative length" of the response function. It indicates the number of elements in the response function array that correspond to negative argument values. Outside the range , the response function is considered zero.
5. int positivelen: This is an integer representing the "positive length" of the response function. It indicates the number of elements in the response function array that correspond to positive argument values. Similar to negativelen, outside the range , the response function is considered zero.
The function works by:
1. Calculating the length nl of the arrays used for FFT, ensuring it's a power of 2 and large enough to hold the signal and response.
2. Creating two new arrays, a1 and a2, of length nl and initializing them with the input signal and response function, respectively.
3. Applying the forward FFT (realfastfouriertransform) to both arrays, a1 and a2.
4. Performing element-wise multiplication of the FFT results in the frequency domain.
5. Applying the inverse FFT (realfastfouriertransform) to the multiplied results in a1.
6. Updating the original signal array with the convolution result, which is stored in the a1 array.
The result of the convolution is stored in the input signal array at the function exit.
Fast Correlation
This code defines a function called fastcorrelation that computes the correlation between a signal and a pattern using the Fast Fourier Transform (FFT) method. The function takes four input arguments and modifies the input signal array to store the correlation values.
Input arguments:
1. float signal: This is an array of real numbers representing the signal to be correlated with the pattern. The elements are numbered from 0 to SignalLen-1.
2. int signallen: This is an integer representing the length of the input signal array.
3. float pattern: This is an array of real numbers representing the pattern to be correlated with the signal. The elements are numbered from 0 to PatternLen-1.
4. int patternlen: This is an integer representing the length of the pattern array.
The function performs the following steps:
1. Calculate the required size nl for the FFT by finding the smallest power of 2 that is greater than or equal to the sum of the lengths of the signal and the pattern.
2. Create two new arrays a1 and a2 with the length nl and initialize them to 0.
3. Copy the signal array into a1 and pad it with zeros up to the length nl.
4. Copy the pattern array into a2 and pad it with zeros up to the length nl.
5. Compute the FFT of both a1 and a2.
6. Perform element-wise multiplication of the frequency-domain representation of a1 and the complex conjugate of the frequency-domain representation of a2.
7. Compute the inverse FFT of the result obtained in step 6.
8. Store the resulting correlation values in the original signal array.
At the end of the function, the signal array contains the correlation values at points from 0 to SignalLen-1.
Fast Fourier Transform of Two Real Functions
This code defines a function called tworealffts that computes the Fast Fourier Transform (FFT) of two real-valued functions (a1 and a2) using a Cooley-Tukey-based radix-2 Decimation in Time (DIT) algorithm. The FFT is a widely used algorithm for computing the discrete Fourier transform (DFT) and its inverse.
Input parameters:
1. float a1: an array of real numbers, representing the values of the first function.
2. float a2: an array of real numbers, representing the values of the second function.
3. float a: an output array to store the Fourier transform of the first function.
4. float b: an output array to store the Fourier transform of the second function.
5. int tn: an integer representing the number of function values. It must be a power of two, but the algorithm doesn't validate this condition.
The function performs the following steps:
1. Combine the two input arrays, a1 and a2, into a single array a by interleaving their elements.
2. Perform a 1D FFT on the combined array a using the radix-2 DIT algorithm.
3. Separate the FFT results of the two input functions from the combined array a and store them in output arrays a and b.
Here is a detailed breakdown of the radix-2 DIT algorithm used in this code:
1. Bit-reverse the order of the elements in the combined array a.
2. Initialize the loop variables mmax, istep, and theta.
3. Enter the main loop that iterates through different stages of the FFT.
a. Compute the sine and cosine values for the current stage using the theta variable.
b. Initialize the loop variables wr and wi for the current stage.
c. Enter the inner loop that iterates through the butterfly operations within each stage.
i. Perform the butterfly operation on the elements of array a.
ii. Update the loop variables wr and wi for the next butterfly operation.
d. Update the loop variables mmax, istep, and theta for the next stage.
4. Separate the FFT results of the two input functions from the combined array a and store them in output arrays a and b.
At the end of the function, the a and b arrays will contain the Fourier transform of the first and second functions, respectively. Note that the function overwrites the input arrays a and b.
█ Example scripts using functions contained in loxxfft
Real-Fast Fourier Transform of Price w/ Linear Regression
Real-Fast Fourier Transform of Price Oscillator
Normalized, Variety, Fast Fourier Transform Explorer
Variety RSI of Fast Discrete Cosine Transform
STD-Stepped Fast Cosine Transform Moving Average
Rsi strategy for BTC with (Rsi SPX)
I hope this strategy is just an idea and a starting point, I use the correlation of the Sp500 with the Btc, this does not mean that this correlation will exist forever!. I love Trading view and I'm learning to program, I find correlations very interesting and here is a simple strategy.
This is a trading strategy script written in Pine Script language for use in TradingView. Here is a brief overview of the strategy:
The script uses the RSI (Relative Strength Index) technical indicator with a period of 14 on two securities: the S&P 500 (SPX) and the symbol corresponding to the current chart (presumably Bitcoin, based on the variable name "Btc_1h_fixed"). The RSI is plotted on the chart for both securities.
The script then sets up two trading conditions using the RSI values:
A long entry condition: when the RSI for the current symbol crosses above the RSI for the S&P 500, a long trade is opened using the "strategy.entry" function.
A short entry condition: when the RSI for the current symbol crosses below the RSI for the S&P 500, a short trade is opened using the "strategy.entry" function.
The script also includes a take profit input parameter that allows the user to set a percentage profit target for closing the trade. The take profit is set using the "strategy.exit" function.
Overall, the strategy aims to take advantage of divergences in RSI values between the current symbol and the S&P 500 by opening long or short trades accordingly. The take profit parameter allows the user to set a specific profit target for each trade. However, the script does not include any stop loss or risk management features, which should be considered when implementing the strategy in a real trading scenario.
