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Ehlers Dominant Cycle Tuned Bypass Filter [CC]The Dominant Cycle Tuned Bypass Filter was created by John Ehlers (Stocks & Commodities V. 26:3 (16-22)) and this is a particularly unique indicator because this does a pretty good job at predicting the future stock movements. If the blue line crosses over the red then a few bars from now the stock price will most likely go up and if the blue line crosses below the red then a few bars from now the stock price should go down. Since this is such a unique indicator to use with entry and exit points, I don't have them color coded but try this out and let me know what you think. This was a special request so let me know what other scripts you would like to see me publish or if you want anything custom done! Note: I'm republishing this because the original script couldn't be found in searches so this will fix that.
Pine Script® indicator
by cheatcountry
Ehlers Correlation Cycle IndicatorThe Correlation Cycle Indicator was created by John Ehlers (Stocks & Commodities V. 38:06 (8–15)) and this is technically part of three indicators in one so I'm splitting each one to a separate script. This particular indicator was designed for trend direction and trend strength and simply buy when it is green and sell when it turns red. Also keep in mind that the higher the indicator is above the signal then the stronger the trend and when they are close together, conditions get choppy. Let me know if you would like to see me publish other scripts or if you want something custom done!
Pine Script® indicator
by cheatcountry
8
ZenTrend Price CyclesZenTrend attempts to plot the cycles that occur as the price cycles between the top and bottom of long- and short-term price linear regression channels. The indicator observes a fast (35-period) and a slow (100-period) linear regression channel and plots their slopes on an oscillator. When the slope of the fast channel crosses above or below the slope of the slow channel, a signal is plotted. The red line is the slope of the fast channel; blue is the slope of the slow channel A green dot and background indicates the slope of recent price action has crossed above the slope of long-term price action. A red dot and background indicates the slope of recent price action has crossed below the slope of long-term price action. A gray dot indicates the slope of recent price action is slowing. The difference between the long- and short-term slopes is narrowing. Here are things I look for when observing price cycles Where does the cross occur? Crosses high above or below the 'zero line' indicate a more extreme change in price channel slopes. Flat line: crosses that occur while the lines are flat often indicate chop. "Curve" of the line - a cross that occurs as the slope lines are starting to curve up/down indicates a sharper and more extreme change in price channel slope.
Pine Script® indicator
by glst0rm
5
[blackcat] L2 Ehlers Phase Accumulator Cycle Period MeasurerLevel: 2 Background John F. Ehlers introuced Phase Accumulation technique of cycle period measurement in his "Rocket Science for Traders" chapter 7. It is perhaps the easiest to comprehend. In this technique, John Ehlers measures the phase at each sample by taking the arctangent of the ratio of the Quadrature component to the In-phase component. A delta phase is generated by taking the difference of the phase between successive samples. At each sample Dr. Ehlers then looks backward, adding up the delta phases. When the sum of the delta phases reaches 360 degrees (2*pi in tradingview), we must have passed through one full cycle, on average. The process is repeated for each new sample. Function blackcat L2 Ehlers Phase Accumulator Cycle Period Measurer is used to measure Dominant Cycle (DC). This is one of John Ehlers three major methods to measure DC. The Phase Accumulation method of cycle measurement always uses one full cycle’s worth of historical data. This is both an advantage and disadvantage. The advantage is the lag in obtaining the answer scales directly with the cycle period. That is, the measurement of a short cycle period has less lag than the measurement of a longer cycle period. However, the number of samples used in making the measurement means the averaging period is variable with cycle period. Longer averaging reduces the noise level compared to the signal. Therefore, shorter cycle periods necessarily have a higher output Signal-to-Noise Ratio (SNR). Key Signal Smooth --> 4 bar WMA w/ 1 bar lag Detrender --> The amplitude response of a minimum-length HT can be improved by adjusting the filter coefficients by trial and error. HT does not allow DC component at zero frequency for transformation. So, Detrender is used to remove DC component/ trend component. Q1 --> Quadrature phase signal I1 --> In-phase signal Period --> Dominant Cycle in bars Pros and Cons 100% John F. Ehlers definition translation of original work, even variable names are the same. This help readers who would like to use pine to read his book. If you had read his works, then you will be quite familiar with my code style. Remarks The 2nd script for Blackcat1402 John F. Ehlers Week publication. Readme In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts. The scripts posted are categorized into 5 levels according to my efforts or manhours put into these works. Level 1 : interesting script snippets or distinctive improvement from classic indicators or strategy. Level 1 scripts can usually appear in more complex indicators as a function module or element. Level 2 : composite indicator/strategy. By selecting or combining several independent or dependent functions or sub indicators in proper way, the composite script exhibits a resonance phenomenon which can filter out noise or fake trading signal to enhance trading confidence level. Level 3 : comprehensive indicator/strategy. They are simple trading systems based on my strategies. They are commonly containing several or all of entry signal, close signal, stop loss, take profit, re-entry, risk management, and position sizing techniques. Even some interesting fundamental and mass psychological aspects are incorporated. Level 4 : script snippets or functions that do not disclose source code. Interesting element that can reveal market laws and work as raw material for indicators and strategies. If you find Level 1~2 scripts are helpful, Level 4 is a private version that took me far more efforts to develop. Level 5 : indicator/strategy that do not disclose source code. private version of Level 3 script with my accumulated script processing skills or a large number of custom functions. I had a private function library built in past two years. Level 5 scripts use many of them to achieve private trading strategy.
Pine Script® indicator
by blackcat1402
1
Enhanced Instantaneous Cycle Period - Dr. John EhlersThis is my first public release of detector code entitled "Enhanced Instantaneous Cycle Period" for PSv4.0 I built many months ago. Be forewarned, this is not an indicator, this is a detector to be used by ADVANCED developers to build futuristic indicators in Pine. The origins of this script come from a document by Dr. John Ehlers entitled "SIGNAL ANALYSIS CONCEPTS". You may find this using the NSA's reverse search engine "goggles", as I call it. John Ehlers' MESA used this measurement to establish the data window for analysis for MESA Cycle computations. So... does any developer wish to emulate MESA Cycle now?? I decided to take instantaneous cycle period to another level of novel attainability in this public release of source code with the following methods, if you are curious how I ENHANCED it. Firstly I reduced the delay of accurate measurement from bar_index==0 by quite a few bars closer to IPO. Secondarily, I provided a limit of 6 for a minimum instantaneous cycle period. At bar_index==0, it would provide a period of 0 wrecking many algorithms from the start. I also increased the instantaneous cycle period's maximum value to 80 from 50, providing a window of 6-80 for the instantaneous cycle period value window limits. Thirdly, I replaced the internal EMA with another algorithm. It reduces the lag while extracting a floating point number, for algorithms that will accept that, compared to a sluggish ordinary EMA return. You will see the excessive EMA delay with adding plot(ema(ICP,7)) as it was originally designed. Lastly it's in one simple function for reusability in a nice little package comprising of less than 40 lines of code. I hope I explained that adequately enough and gave you the reader a glimpse of the "Power of Pine" combined with ingenuity. Be forewarned again, that most of Pine's built-in functions will not accept a floating-point number or dynamic integers for the "length" of it's calculation. You will have to emulate the built-in functions by creating Pine based custom functions, and I assure you, this is very possible in many cases, but not all without array support. You may use int(ICP) to extract an integer from the smoothICP return variable, which may be favorable compared to the choppiness/ringing if ICP alone. This is commonly what my dense intricate code looks like behind the veil. If you are wondering why there is barely any notation, that's because the notation is in the variable naming and this is intended primarily for ADVANCED developers too. It does contain lines of code that explore techniques in Pine that may be applicable in other Pine projects for those learning or wishing to excel with Pine. Showcased in the chart below is my free to use "Enhanced Schaff Trend Cycle Indicator", having a common appeal to TV users frequently. If you do have any questions or comments regarding this indicator, I will consider your inquiries, thoughts, and ideas presented below in the comments section, when time provides it. As always, "Like" it if you simply just like it with a proper thumbs up, and also return to my scripts list occasionally for additional postings. Have a profitable future everyone! NOTICE: Copy pasting bandits who may be having nefarious thoughts, DO NOT attempt this, because this may violate Tradingview's terms, conditions and/or house rules. "WE" are always watching the TV community vigilantly for mischievous behaviors and actions that exploit well intended authors for the purpose of increasing brownie points in reputation scores. Hiding behind a "protected" wall may not protect you from investigation and account penalization by TV staff. Be respectful, and don't just throw an ma() in there branding it as "your" gizmo. Fair enough? Alrighty then... I firmly believe in "innovating" future state-of-the-art indicators, and please contact me if you wish to do so.
Pine Script® indicator
by ImmortalFreedom
1
[FS] Time & Cycles Time & Cycles A comprehensive trading session indicator that helps traders identify and track key market sessions and their price levels. This tool is particularly useful for forex and futures traders who need to monitor multiple trading sessions. Key Features: • Multiple Session Support: - London Session - New York Session - Sydney Session - Asia Session - Customizable TBD Session • Session Visualization: - Clear session boxes with customizable colors - Session labels with adjustable visibility - Support for sessions crossing midnight - Timezone-aware calculations • Price Level Tracking: - Daily High/Low levels - Weekly High/Low levels - Previous session High/Low levels - Customizable history depth for each level type • Customization Options: - Adjustable colors for each session - Customizable border styles - Label visibility controls - Timezone selection - History level depth settings • Technical Features: - High-performance calculation engine - Support for multiple timeframes - Efficient memory usage - Clean and intuitive visual display Perfect for: • Forex traders monitoring multiple sessions • Futures traders tracking market hours • Swing traders identifying key session levels • Day traders planning their trading hours • Market analysts studying session patterns The indicator helps traders: - Identify active trading sessions - Track session-specific price levels - Monitor market activity across different time zones - Plan trades based on session boundaries - Analyze price action within specific sessions Note: This indicator is designed to work across all timeframes and is optimized for performance with minimal impact on chart loading times.
Pine Script® indicator
by SF_Trade
2
Hosoda Cycles (24x7 mkt) {fmz}This script allows you to see on the chart which are the bars, including future ones, which correspond to the cycles of Goichi Hosoda, the inventor of Ichimoku Kinko Hyo. This script is only suitable for 24x7 markets, it is not suitable for markets with closing times and weekends, or gap markets where trading is not active. In fact, the calculation of calendar times is used, not suitable for markets with closing times. Use the settings to indicate what the start time of bar 1. The indicator will produce many vertical bars, even in addition to the end time of the graph.
Pine Script® indicator
by franzb0
4
[blackcat] L2 Ehlers Dual Differential Cycle Period MeasurerLevel: 2 Background John F. Ehlers introuced Dual Differential Cycle Period Measurer in his "Rocket Science for Traders" chapter 7. The In-phase and Quadrature components are computed with the Hilbert Transformer using procedures identical to those in the Dual Differentiator. Function blackcat L2 Ehlers Homodyne Discriminator Cycle Period Measurer is used to measure Dominant Cycle (DC). This is one of John Ehlers three major methods to measure DC. These components undergo a complex averaging and are smoothed in an EMA to avoid any undesired cross products in the multiplication step that follows. The period is solved directly from the smoothed Inphase and Quadrature components. The interim calculation for the denominator is performed as Value1 to ensure that the denominator will not have a zero value. The sign of Valuel is reversed relative to the theoretical equation because the differences are looking backward in time. Key Signal Smooth --> 4 bar WMA w/ 1 bar lag Detrender --> The amplitude response of a minimum-length HT can be improved by adjusting the filter coefficients by trial and error. HT does not allow DC component at zero frequency for transformation. So, Detrender is used to remove DC component/ trend component. Q1 --> Quadrature phase signal I1 --> In-phase signal Period --> Dominant Cycle in bars SmoothPeriod --> Period with complex averaging Pros and Cons 100% John F. Ehlers definition translation of original work, even variable names are the same. This help readers who would like to use pine to read his book. If you had read his works, then you will be quite familiar with my code style. Remarks The 4th script for Blackcat1402 John F. Ehlers Week publication. Readme In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts. The scripts posted are categorized into 5 levels according to my efforts or manhours put into these works. Level 1 : interesting script snippets or distinctive improvement from classic indicators or strategy. Level 1 scripts can usually appear in more complex indicators as a function module or element. Level 2 : composite indicator/strategy. By selecting or combining several independent or dependent functions or sub indicators in proper way, the composite script exhibits a resonance phenomenon which can filter out noise or fake trading signal to enhance trading confidence level. Level 3 : comprehensive indicator/strategy. They are simple trading systems based on my strategies. They are commonly containing several or all of entry signal, close signal, stop loss, take profit, re-entry, risk management, and position sizing techniques. Even some interesting fundamental and mass psychological aspects are incorporated. Level 4 : script snippets or functions that do not disclose source code. Interesting element that can reveal market laws and work as raw material for indicators and strategies. If you find Level 1~2 scripts are helpful, Level 4 is a private version that took me far more efforts to develop. Level 5 : indicator/strategy that do not disclose source code. private version of Level 3 script with my accumulated script processing skills or a large number of custom functions. I had a private function library built in past two years. Level 5 scripts use many of them to achieve private trading strategy.
Pine Script® indicator
by blackcat1402
Bollinger Breaks and Cycles Indicator - JDThe BBC indicator shows price in relation to the upper (in red) and lower (in green) Bollinger Bands It highlights breaks in the Bands, where the 0-line represents a price equal to the band. These breaks can either be used as take-profit points or as entry points, depending on trend direction. Entries can be at the beginning of a break (eg. for impulse or continuation moves) or at the end (mostly for expected trend reversals) To find the best setups, the BBC should be accompanied by other indicators (preferably ones that focus on different aspects) The oscilating line in the middle indicates market cycles JD. #NotTradingAdvice #DYOR
Pine Script® indicator
by Duyck
4
Ehlers Cyber Cycle Indicator [LazyBear]The Cyber Cycle Indicator, developed by John Ehlers, is used for isolating the cycle component of the market from its trend counterpart. Unlike other oscillators like RSI, Cyber Cycle Indicator's wave has a variable amplitude. Use the osc/signal crossover for entry/exit points. You can enable highlighting the crossovers by using region fills (via options page). I have also added an option to color the bars based on this. Actually I have lot of Ehlers indicators in my to-publish backlog, will try to prioritize them over the others in the pipeline. Lets have an Ehlers week for indicators :) More info: Cybernetic Analysis for Stocks and Futures List of my public indicators: bit.ly List of my app-store indicators: blog.tradingview.com
Pine Script® indicator
by LazyBear
8
B3 Bar Cycle MTF (fix)Apologies, there was an error in printing for the thick gray boxes, happened when MTF was switched on. All better, and here is the details from before: This is an interesting study that can be used as a tool for determining trend direction, and also could be a trailing stop setter. I use it as a gauge on MTF settings. If on, you can look at the bar cycle of the 1h while on the 15m giving you a lot of information in one tool. If a line is missing high or low, it is because it was broken, if both exist you are trading in range and cloud appears. If both sides break you get thick gray boxes above and below bar. Get used to editing the inputs to suit your liking. Often 3-5 length and always looking at different resolutions to get a big picture story. You could put multiple instances of the study up to see them simultaneously. I based the idea off of Krausz's 3 day cycle which you can read about in his teachings. I tend to find it looking better using Heikin Ashi bar-style.
Pine Script® indicator
by HammondB3
5
B3 Bar Cycle MTFThis is an interesting study that can be used as a tool for determining trend direction, and also could be a trailing stop setter. I use it as a gauge on MTF settings, in the pic MTF is turned off. If on, you can look at the bar cycle of the 1h while on the 15m giving you a lot of information in one tool. If a line is missing high or low, it is because it was broken, if both exist you are trading in range and cloud appears. If both sides break you get thick gray boxes above and below bar. Get used to editing the inputs to suit your liking. Often 3-5 length and always looking at different resolutions to get a big picture story. You could put multiple instances of the study up to see them simultaneously. I based the idea off of Krausz's 3 day cycle which you can read about in his teachings. I tend to find it looking better using Heikin Ashi bar-style.
Pine Script® indicator
by HammondB3
2
Sharktank - Pi Cycle PredictionThe Pi Cycle indicator has called tops in Bitcoin quite accurately. Assuming history repeats itself, knowledge about when it might happen again could benefit you. The indicator is fairly simple: - A daily moving average of 350 ("long_ma" in script) - A daily moving average of 111 ("short_ma" in script) The value of the long moving average is multiplied by two. This way the longer moving average appears above the shorter one. When the shorter one (orange colored) crosses above the longer (green colored) one, it could mean the top is in. These moving averages rise at a certain rate. Using these rates we could try to estimate a possible crossover moment. That's exactly what this indicator does! It gives the user a prediction of when a crossover might happen. Special thanks to: - Ninorigo, for making his indicator public. This one uses his as a starting point. - The_Caretaker, for coming up with this idea about calling a top. Yet, his is more price-based, this one is more time-based.
Pine Script® indicator
by Bluntpiloot
25
Correlation Cycle, CorrelationAngle, Market State - John EhlersHot off the press, I present this "Correlation Cycle, CorrelationAngle, and Market State" multicator employing PSv4.0, originally formulated by Dr. John Ehlers for TASC - June 2020 Traders Tips. Basically it's an all-in-one combination of three Ehlers' indicators. This power packed triplet indicator, being less than a 100 line implementation at initial release, is a heavily modified version of the original indicator using novel techniques that surpass John Ehlers' original intended design. This is also a profound script in numerous ways. First of all, these three indicators are directly from the illustrious mastermind himself Dr. John Ehlers. Secondarily, this is my "50th" script published on TV, which makes it even more significant. I'm especially proud of this script to "degrees" of imagination I once didn't know was theoretically possible in code. My intellect has once again been mathemagically unlocked pondering new innovations with this code revelation. Thirdly, this PSv4.0 script shows the empowering beauty and elegance of hacking the stock markets with TV's ultra utilitarian Pine Editor(PE) in a common browser! Some of you may be wondering if I worked on this for days... nope! This only took a few hours, followed by writing this description for another hour plus. I have created many of Ehlers' indicators in PE, a few of which I have published in my profile, but I wanted to show how programming with Pine Script can be an artistic form of craftsmanship and poetry. None of this would be possible without the ingeniously minded Tradingview staff revolutionizing algorithmic trading at it's finest. If you should ever encounter them by chance, ponder humbly thanking these computing wizards for their diligence and dedication. They are providing, and shall award to us members, some of the most fascinating conceptualized tech imaginable in the coming future. I can assure you, much, much more is yet to be unveiled for us TV members/enthusiasts. Thank you TV and all you offer to this community. As always, I have included advanced Pine programming techniques that conform to proper "Pine Etiquette" by example. There are so many Pine mastery techniques included, I don't have an abundance of time to elaborate on all of them. For those of you are code savvy, you may have notice I only used one "for" loop for increased server efficiency, instead of the two "for" loops in the original formulation. For those of you who are newcomers to Pine Script, this code release may also help you comprehend the immense "Power of Pine" by employing advanced programming techniques while exhibiting code utilization in a most effective manner. This is commonly what my dense intricate code looks like behind the veil. If you are wondering why there is hardly any notes, that's because the notation is primarily in the variable naming. Features List Includes: Dark Background - Easily disabled in indicator Settings->Style for "Light" charts or with Pine commenting AND a few more... Why list them, when you have the source code! The comments section below is solely just for commenting and other remarks, ideas, compliments, etc... regarding only this indicator, not others. When available time provides itself, I will consider your inquiries, thoughts, and concepts presented below in the comments section, should you have any questions or comments regarding this indicator. When my indicators achieve more prevalent use by TV members, I may implement more ideas when they present themselves as worthy additions. As always, "Like" it if you simply just like it with a proper thumbs up, and also return to my scripts list occasionally for additional postings. Have a profitable future everyone!
Pine Script® indicator
by ImmortalFreedom
27
Ehlers Autocorrelation Periodogram (EACP)# EACP: Ehlers Autocorrelation Periodogram ## Overview and Purpose Developed by John F. Ehlers (Technical Analysis of Stocks & Commodities, Sep 2016), the Ehlers Autocorrelation Periodogram (EACP) estimates the dominant market cycle by projecting normalized autocorrelation coefficients onto Fourier basis functions. The indicator blends a roofing filter (high-pass + Super Smoother) with a compact periodogram, yielding low-latency dominant cycle detection suitable for adaptive trading systems. Compared with Hilbert-based methods, the autocorrelation approach resists aliasing and maintains stability in noisy price data. EACP answers a central question in cycle analysis: “What period currently dominates the market?” It prioritizes spectral power concentration, enabling downstream tools (adaptive moving averages, oscillators) to adjust responsively without the lag present in sliding-window techniques. ## Core Concepts * **Roofing Filter:** High-pass plus Super Smoother combination removes low-frequency drift while limiting aliasing. * **Pearson Autocorrelation:** Computes normalized lag correlation to remove amplitude bias. * **Fourier Projection:** Sums cosine and sine terms of autocorrelation to approximate spectral energy. * **Gain Normalization:** Automatic gain control prevents stale peaks from dominating power estimates. * **Warmup Compensation:** Exponential correction guarantees valid output from the very first bar. ## Implementation Notes **This is not a strict implementation of the TASC September 2016 specification.** It is a more advanced evolution combining the core 2016 concept with techniques Ehlers introduced later. The fundamental Wiener-Khinchin theorem (power spectral density = Fourier transform of autocorrelation) is correctly implemented, but key implementation details differ: ### Differences from Original 2016 TASC Article 1. **Dominant Cycle Calculation:** - **2016 TASC:** Uses peak-finding to identify the period with maximum power - **This Implementation:** Uses Center of Gravity (COG) weighted average over bins where power ≥ 0.5 - **Rationale:** COG provides smoother transitions and reduces susceptibility to noise spikes 2. **Roofing Filter:** - **2016 TASC:** Simple first-order high-pass filter - **This Implementation:** Canonical 2-pole high-pass with √2 factor followed by Super Smoother bandpass - **Formula:** `hp := (1-α/2)²·(p-2p +p ) + 2(1-α)·hp - (1-α)²·hp ` - **Rationale:** Evolved filtering provides better attenuation and phase characteristics 3. **Normalized Power Reporting:** - **2016 TASC:** Reports peak power across all periods - **This Implementation:** Reports power specifically at the dominant period - **Rationale:** Provides more meaningful correlation between dominant cycle strength and normalized power 4. **Automatic Gain Control (AGC):** - Uses decay factor `K = 10^(-0.15/diff)` where `diff = maxPeriod - minPeriod` - Ensures K < 1 for proper exponential decay of historical peaks - Prevents stale peaks from dominating current power estimates ### Performance Characteristics - **Complexity:** O(N²) where N = (maxPeriod - minPeriod) - **Implementation:** Uses `var` arrays with native PineScript historical operator ` ` - **Warmup:** Exponential compensation (§2 pattern) ensures valid output from bar 1 ### Related Implementations This refined approach aligns with: - TradingView TASC 2025.02 implementation by blackcat1402 - Modern Ehlers cycle analysis techniques post-2016 - Evolved filtering methods from *Cycle Analytics for Traders* The code is mathematically sound and production-ready, representing a refined version of the autocorrelation periodogram concept rather than a literal translation of the 2016 article. ## Common Settings and Parameters | Parameter | Default | Function | When to Adjust | |-----------|---------|----------|---------------| | Min Period | 8 | Lower bound of candidate cycles | Increase to ignore microstructure noise; decrease for scalping. | | Max Period | 48 | Upper bound of candidate cycles | Increase for swing analysis; decrease for intraday focus. | | Autocorrelation Length | 3 | Averaging window for Pearson correlation | Set to 0 to match lag, or enlarge for smoother spectra. | | Enhance Resolution | true | Cubic emphasis to highlight peaks | Disable when a flatter spectrum is desired for diagnostics. | **Pro Tip:** Keep `(maxPeriod - minPeriod)` ≤ 64 to control $O(n^2)$ inner loops and maintain responsiveness on lower timeframes. ## Calculation and Mathematical Foundation **Explanation:** 1. Apply roofing filter to `source` using coefficients $\alpha_1$, $a_1$, $b_1$, $c_1$, $c_2$, $c_3$. 2. For each lag $L$ compute Pearson correlation $r_L$ over window $M$ (default $L$). 3. For each period $p$, project onto Fourier basis: $C_p=\sum_{n=2}^{N} r_n \cos\left(\frac{2\pi n}{p}\right)$ and $S_p=\sum_{n=2}^{N} r_n \sin\left(\frac{2\pi n}{p}\right)$. 4. Power $P_p=C_p^2+S_p^2$, smoothed then normalized via adaptive peak tracking. 5. Dominant cycle $D=\frac{\sum p\,\tilde P_p}{\sum \tilde P_p}$ over bins where $\tilde P_p≥0.5$, warmup-compensated. **Technical formula:** ``` Step 1: hp_t = ((1-α₁)/2)(src_t - src_{t-1}) + α₁ hp_{t-1} Step 2: filt_t = c₁(hp_t + hp_{t-1})/2 + c₂ filt_{t-1} + c₃ filt_{t-2} Step 3: r_L = (M Σxy - Σx Σy) / √ Step 4: P_p = (Σ_{n=2}^{N} r_n cos(2πn/p))² + (Σ_{n=2}^{N} r_n sin(2πn/p))² Step 5: D = Σ_{p∈Ω} p · ĤP_p / Σ_{p∈Ω} ĤP_p with warmup compensation ``` > 🔍 **Technical Note:** Warmup uses $c = 1 / (1 - (1 - \alpha)^{k})$ to scale early-cycle estimates, preventing low values during initial bars. ## Interpretation Details - **Primary Dominant Cycle:** - High $D$ (e.g., > 30) implies slow regime; adaptive MAs should lengthen. - Low $D$ (e.g., < 15) signals rapid oscillations; shorten lookback windows. - **Normalized Power:** - Values > 0.8 indicate strong cycle confidence; consider cyclical strategies. - Values < 0.3 warn of flat spectra; favor trend or volatility approaches. - **Regime Shifts:** - Rapid drop in $D$ alongside rising power often precedes volatility expansion. - Divergence between $D$ and price swings may highlight upcoming breakouts. ## Limitations and Considerations - **Spectral Leakage:** Limited lag range can smear peaks during abrupt volatility shifts. - **O(n²) Segment:** Although constrained (≤ 60 loops), wide period spans increase computation. - **Stationarity Assumption:** Autocorrelation presumes quasi-stationary cycles; regime changes reduce accuracy. - **Latency in Noise:** Even with roofing, extremely noisy assets may require higher `avgLength`. - **Downtrend Bias:** Negative trends may clip high-pass output; ensure preprocessing retains signal. ## References * Ehlers, J. F. (2016). “Past Market Cycles.” *Technical Analysis of Stocks & Commodities*, 34(9), 52-55. * Thinkorswim Learning Center. “Ehlers Autocorrelation Periodogram.” * Fab MacCallini. “autocorrPeriodogram.R.” GitHub repository. * QuantStrat TradeR Blog. “Autocorrelation Periodogram for Adaptive Lookbacks.” * TradingView Script by blackcat1402. “Ehlers Autocorrelation Periodogram (Updated).”
Pine Script® indicator
by mihakralj