Adaptive Look-back/Volatility Phase Change Index on Jurik [Loxx]Adaptive Look-back, Adaptive Volatility Phase Change Index on Jurik is a Phase Change Index but with adaptive length and volatility inputs to reduce phase change noise and better identify trends. This is an invese indicator which means that small values on the oscillator indicate bullish sentiment and higher values on the oscillator indicate bearish sentiment
What is the Phase Change Index?
Based on the M.H. Pee's TASC article "Phase Change Index".
Prices at any time can be up, down, or unchanged. A period where market prices remain relatively unchanged is referred to as a consolidation. A period that witnesses relatively higher prices is referred to as an uptrend, while a period of relatively lower prices is called a downtrend.
The Phase Change Index (PCI) is an indicator designed specifically to detect changes in market phases.
This indicator is made as he describes it with one deviation: if we follow his formula to the letter then the "trend" is inverted to the actual market trend. Because of that an option to display inverted (and more logical) values is added.
What is the Jurik Moving Average?
Have you noticed how moving averages add some lag (delay) to your signals? ... especially when price gaps up or down in a big move, and you are waiting for your moving average to catch up? Wait no more! JMA eliminates this problem forever and gives you the best of both worlds: low lag and smooth lines.
Ideally, you would like a filtered signal to be both smooth and lag-free. Lag causes delays in your trades, and increasing lag in your indicators typically result in lower profits. In other words, late comers get what's left on the table after the feast has already begun.
That's why investors, banks and institutions worldwide ask for the Jurik Research Moving Average ( JMA ). You may apply it just as you would any other popular moving average. However, JMA's improved timing and smoothness will astound you.
What is adaptive Jurik volatility
One of the lesser known qualities of Juirk smoothing is that the Jurik smoothing process is adaptive. "Jurik Volty" (a sort of market volatility ) is what makes Jurik smoothing adaptive. The Jurik Volty calculation can be used as both a standalone indicator and to smooth other indicators that you wish to make adaptive.
What is an adaptive cycle, and what is Ehlers Autocorrelation Periodogram Algorithm?
From his Ehlers' book Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers, 2013, page 135:
"Adaptive filters can have several different meanings. For example, Perry Kaufman’s adaptive moving average (KAMA) and Tushar Chande’s variable index dynamic average (VIDYA) adapt to changes in volatility. By definition, these filters are reactive to price changes, and therefore they close the barn door after the horse is gone.The adaptive filters discussed in this chapter are the familiar Stochastic, relative strength index (RSI), commodity channel index (CCI), and band-pass filter.The key parameter in each case is the look-back period used to calculate the indicator. This look-back period is commonly a fixed value. However, since the measured cycle period is changing, it makes sense to adapt these indicators to the measured cycle period. When tradable market cycles are observed, they tend to persist for a short while.Therefore, by tuning the indicators to the measure cycle period they are optimized for current conditions and can even have predictive characteristics.
The dominant cycle period is measured using the Autocorrelation Periodogram Algorithm. That dominant cycle dynamically sets the look-back period for the indicators. I employ my own streamlined computation for the indicators that provide smoother and easier to interpret outputs than traditional methods. Further, the indicator codes have been modified to remove the effects of spectral dilation.This basically creates a whole new set of indicators for your trading arsenal."
Included
-Your choice of length input calculation, either fixed or adaptive cycle
-Invert the signal to match the trend
-Bar coloring to paint the trend
Happy trading!

# Dominantcycle

Ehlers Autocorrelation Periodogram [Loxx]Ehlers Autocorrelation Periodogram contains two versions of Ehlers Autocorrelation Periodogram Algorithm. This indicator is meant to supplement adaptive cycle indicators that myself and others have published on Trading View, will continue to publish on Trading View. These are fast-loading, low-overhead, streamlined, exact replicas of Ehlers' work without any other adjustments or inputs.
Versions:
- 2013, Cycle Analytics for Traders Advanced Technical Trading Concepts by John F. Ehlers
- 2016, TASC September, "Measuring Market Cycles"
Description
The Ehlers Autocorrelation study is a technical indicator used in the calculation of John F. Ehlers’s Autocorrelation Periodogram. Its main purpose is to eliminate noise from the price data, reduce effects of the “spectral dilation” phenomenon, and reveal dominant cycle periods. The spectral dilation has been discussed in several studies by John F. Ehlers; for more information on this, refer to sources in the "Further Reading" section.
As the first step, Autocorrelation uses Mr. Ehlers’s previous installment, Ehlers Roofing Filter, in order to enhance the signal-to-noise ratio and neutralize the spectral dilation. This filter is based on aerospace analog filters and when applied to market data, it attempts to only pass spectral components whose periods are between 10 and 48 bars.
Autocorrelation is then applied to the filtered data: as its name implies, this function correlates the data with itself a certain period back. As with other correlation techniques, the value of +1 would signify the perfect correlation and -1, the perfect anti-correlation.
Using values of Autocorrelation in Thermo Mode may help you reveal the cycle periods within which the data is best correlated (or anti-correlated) with itself. Those periods are displayed in the extreme colors (orange) while areas of intermediate colors mark periods of less useful cycles.
What is an adaptive cycle, and what is the Autocorrelation Periodogram Algorithm?
From his Ehlers' book mentioned above, page 135:
"Adaptive filters can have several different meanings. For example, Perry Kaufman’s adaptive moving average ( KAMA ) and Tushar Chande’s variable index dynamic average ( VIDYA ) adapt to changes in volatility . By definition, these filters are reactive to price changes, and therefore they close the barn door after the horse is gone.The adaptive filters discussed in this chapter are the familiar Stochastic , relative strength index ( RSI ), commodity channel index ( CCI ), and band-pass filter.The key parameter in each case is the look-back period used to calculate the indicator.This look-back period is commonly a fixed value. However, since the measured cycle period is changing, as we have seen in previous chapters, it makes sense to adapt these indicators to the measured cycle period. When tradable market cycles are observed, they tend to persist for a short while.Therefore, by tuning the indicators to the measure cycle period they are optimized for current conditions and can even have predictive characteristics.
The dominant cycle period is measured using the Autocorrelation Periodogram Algorithm. That dominant cycle dynamically sets the look-back period for the indicators. I employ my own streamlined computation for the indicators that provide smoother and easier to interpret outputs than traditional methods. Further, the indicator codes have been modified to remove the effects of spectral dilation.This basically creates a whole new set of indicators for your trading arsenal."
How to use this indicator
The point of the Ehlers Autocorrelation Periodogram Algorithm is to dynamically set a period between a minimum and a maximum period length. While I leave the exact explanation of the mechanic to Dr. Ehlers’s book, for all practical intents and purposes, in my opinion, the punchline of this method is to attempt to remove a massive source of overfitting from trading system creation–namely specifying a look-back period. SMA of 50 days? 100 days? 200 days? Well, theoretically, this algorithm takes that possibility of overfitting out of your hands. Simply, specify an upper and lower bound for your look-back, and it does the rest. In addition, this indicator tells you when its best to use adaptive cycle inputs for your other indicators.
Usage Example 1
Let's say you're using "Adaptive Qualitative Quantitative Estimation (QQE) ". This indicator has the option of adaptive cycle inputs. When the "Ehlers Autocorrelation Periodogram " shows a period of high correlation that adaptive cycle inputs work best during that period.
Usage Example 2
Check where the dominant cycle line lines, grab that output number and inject it into your other standard indicators for the length input.

Adaptive Qualitative Quantitative Estimation (QQE) [Loxx]Adaptive QQE is a fixed and cycle adaptive version of the popular Qualitative Quantitative Estimation (QQE) used by forex traders. This indicator includes varoius types of RSI caculations and adaptive cycle measurements to find tune your signal.
Qualitative Quantitative Estimation (QQE):
The Qualitative Quantitative Estimation (QQE) indicator works like a smoother version of the popular Relative Strength Index (RSI) indicator. QQE expands on RSI by adding two volatility based trailing stop lines. These trailing stop lines are composed of a fast and a slow moving Average True Range (ATR).
There are many indicators for many purposes. Some of them are complex and some are comparatively easy to handle. The QQE indicator is a really useful analytical tool and one of the most accurate indicators. It offers numerous strategies for using the buy and sell signals. Essentially, it can help detect trend reversal and enter the trade at the most optimal positions.
Wilders' RSI:
The Relative Strength Index ( RSI ) is a well versed momentum based oscillator which is used to measure the speed (velocity) as well as the change (magnitude) of directional price movements. Essentially RSI , when graphed, provides a visual mean to monitor both the current, as well as historical, strength and weakness of a particular market. The strength or weakness is based on closing prices over the duration of a specified trading period creating a reliable metric of price and momentum changes. Given the popularity of cash settled instruments (stock indexes) and leveraged financial products (the entire field of derivatives); RSI has proven to be a viable indicator of price movements.
RSX RSI:
RSI is a very popular technical indicator, because it takes into consideration market speed, direction and trend uniformity. However, the its widely criticized drawback is its noisy (jittery) appearance. The Jurk RSX retains all the useful features of RSI , but with one important exception: the noise is gone with no added lag.
Rapid RSI:
Rapid RSI Indicator, from Ian Copsey's article in the October 2006 issue of Stocks & Commodities magazine.
RapidRSI resembles Wilder's RSI , but uses a SMA instead of a WilderMA for internal smoothing of price change accumulators.
VHF Adaptive Cycle:
Vertical Horizontal Filter (VHF) was created by Adam White to identify trending and ranging markets. VHF measures the level of trend activity, similar to ADX DI. Vertical Horizontal Filter does not, itself, generate trading signals, but determines whether signals are taken from trend or momentum indicators. Using this trend information, one is then able to derive an average cycle length.
Band-pass Adaptive Cycle:
Even the most casual chart reader will be able to spot times when the market is cycling and other times when longer-term trends are in play. Cycling markets are ideal for swing trading however attempting to “trade the swing” in a trending market can be a recipe for disaster. Similarly, applying trend trading techniques during a cycling market can equally wreak havoc in your account. Cycle or trend modes can readily be identified in hindsight. But it would be useful to have an objective scientific approach to guide you as to the current market mode.
There are a number of tools already available to differentiate between cycle and trend modes. For example, measuring the trend slope over the cycle period to the amplitude of the cyclic swing is one possibility.
We begin by thinking of cycle mode in terms of frequency or its inverse, periodicity. Since the markets are fractal ; daily, weekly, and intraday charts are pretty much indistinguishable when time scales are removed. Thus it is useful to think of the cycle period in terms of its bar count. For example, a 20 bar cycle using daily data corresponds to a cycle period of approximately one month.
When viewed as a waveform, slow-varying price trends constitute the waveform's low frequency components and day-to-day fluctuations (noise) constitute the high frequency components. The objective in cycle mode is to filter out the unwanted components--both low frequency trends and the high frequency noise--and retain only the range of frequencies over the desired swing period. A filter for doing this is called a bandpass filter and the range of frequencies passed is the filter's bandwidth.
Included:
-Toggle on/off bar coloring
-Customize RSI signal using fixed, VHF Adaptive, and Band-pass Adaptive calculations
-Choose from three different RSI types
Visuals:
-Red/Green line is the moving average of RSI
-Thin white line is the fast trend
-Dotted yellow line is the slow trend
Happy trading!

Aroon Oscillator of Adaptive RSI [Loxx]Aroon Oscillator of Adaptive RSI uses RSI to calculate AROON in attempt to capture more trend and momentum quicker than Aroon or RSI alone. Aroon Oscillator of Adaptive RSI has three different types of RSI calculations and the choice of either fixed, VHF Adaptive, or Band-pass Adaptive cycle measures to calculate RSI.
Arron Oscillator:
The Aroon Oscillator was developed by Tushar Chande in 1995 as part of the Aroon Indicator system. Chande’s intention for the system was to highlight short-term trend changes. The name Aroon is derived from the Sanskrit language and roughly translates to “dawn’s early light.”
The Aroon Oscillator is a trend-following indicator that uses aspects of the Aroon Indicator (Aroon Up and Aroon Down) to gauge the strength of a current trend and the likelihood that it will continue.
Aroon oscillator readings above zero indicate that an uptrend is present, while readings below zero indicate that a downtrend is present. Traders watch for zero line crossovers to signal potential trend changes. They also watch for big moves, above 50 or below -50 to signal strong price moves.
Wilders' RSI:
The Relative Strength Index (RSI) is a well versed momentum based oscillator which is used to measure the speed (velocity) as well as the change (magnitude) of directional price movements. Essentially RSI, when graphed, provides a visual mean to monitor both the current, as well as historical, strength and weakness of a particular market. The strength or weakness is based on closing prices over the duration of a specified trading period creating a reliable metric of price and momentum changes. Given the popularity of cash settled instruments (stock indexes) and leveraged financial products (the entire field of derivatives); RSI has proven to be a viable indicator of price movements.
RSX RSI:
RSI is a very popular technical indicator, because it takes into consideration market speed, direction and trend uniformity. However, the its widely criticized drawback is its noisy (jittery) appearance. The Jurk RSX retains all the useful features of RSI, but with one important exception: the noise is gone with no added lag.
Rapid RSI:
Rapid RSI Indicator, from Ian Copsey's article in the October 2006 issue of Stocks & Commodities magazine.
RapidRSI resembles Wilder's RSI, but uses a SMA instead of a WilderMA for internal smoothing of price change accumulators.
VHF Adaptive Cycle:
Vertical Horizontal Filter (VHF) was created by Adam White to identify trending and ranging markets. VHF measures the level of trend activity, similar to ADX DI. Vertical Horizontal Filter does not, itself, generate trading signals, but determines whether signals are taken from trend or momentum indicators. Using this trend information, one is then able to derive an average cycle length.
Band-pass Adaptive Cycle
Even the most casual chart reader will be able to spot times when the market is cycling and other times when longer-term trends are in play. Cycling markets are ideal for swing trading however attempting to “trade the swing” in a trending market can be a recipe for disaster. Similarly, applying trend trading techniques during a cycling market can equally wreak havoc in your account. Cycle or trend modes can readily be identified in hindsight. But it would be useful to have an objective scientific approach to guide you as to the current market mode.
There are a number of tools already available to differentiate between cycle and trend modes. For example, measuring the trend slope over the cycle period to the amplitude of the cyclic swing is one possibility.
We begin by thinking of cycle mode in terms of frequency or its inverse, periodicity. Since the markets are fractal ; daily, weekly, and intraday charts are pretty much indistinguishable when time scales are removed. Thus it is useful to think of the cycle period in terms of its bar count. For example, a 20 bar cycle using daily data corresponds to a cycle period of approximately one month.
When viewed as a waveform, slow-varying price trends constitute the waveform's low frequency components and day-to-day fluctuations (noise) constitute the high frequency components. The objective in cycle mode is to filter out the unwanted components--both low frequency trends and the high frequency noise--and retain only the range of frequencies over the desired swing period. A filter for doing this is called a bandpass filter and the range of frequencies passed is the filter's bandwidth.
Included:
-Toggle on/off bar coloring
-Customize RSI signal using fixed, VHF Adaptive, and Band-pass Adaptive calculations
-Choose from three different RSI types
Happy trading!

Adaptive, Zero lag Schaff Trend Cycle [Loxx]TASC's March 2008 edition Traders' Tips includes an article by John Ehlers titled "Measuring Cycle Periods," and describes the use of bandpass filters to estimate the length, in bars, of the currently dominant price cycle.
What are Dominant Cycles and Why should we use them?
Even the most casual chart reader will be able to spot times when the market is cycling and other times when longer-term trends are in play. Cycling markets are ideal for swing trading however attempting to “trade the swing” in a trending market can be a recipe for disaster. Similarly, applying trend trading techniques during a cycling market can equally wreak havoc in your account. Cycle or trend modes can readily be identified in hindsight. But it would be useful to have an objective scientific approach to guide you as to the current market mode.
There are a number of tools already available to differentiate between cycle and trend modes. For example, measuring the trend slope over the cycle period to the amplitude of the cyclic swing is one possibility.
We begin by thinking of cycle mode in terms of frequency or its inverse, periodicity. Since the markets are fractal ; daily, weekly, and intraday charts are pretty much indistinguishable when time scales are removed. Thus it is useful to think of the cycle period in terms of its bar count. For example, a 20 bar cycle using daily data corresponds to a cycle period of approximately one month.
When viewed as a waveform, slow-varying price trends constitute the waveform's low frequency components and day-to-day fluctuations (noise) constitute the high frequency components. The objective in cycle mode is to filter out the unwanted components--both low frequency trends and the high frequency noise--and retain only the range of frequencies over the desired swing period. A filter for doing this is called a bandpass filter and the range of frequencies passed is the filter's bandwidth.
Indicator Features
-Zero lag or Regular Schaff Trend Cycle calculation
- Fixed or Band-pass Dominant Cycle for Schaff Trend Cycle MA period inputs
-10 different moving average options for Zero lag calculations
-Separate Band-pass Dominant Cycle calculations for both Schaff Trend Cycle and MA calculations
- Slow-to-Fast Band-pass Dominant Cycle input to tweak the ratio of Schaff Trend Cycle MA input periods as they relate to each other

Hybrid, Zero lag, Adaptive cycle MACD [Loxx]TASC's March 2008 edition Traders' Tips includes an article by John Ehlers titled "Measuring Cycle Periods," and describes the use of bandpass filters to estimate the length, in bars, of the currently dominant price cycle.
What are Dominant Cycles and Why should we use them?
Even the most casual chart reader will be able to spot times when the market is cycling and other times when longer-term trends are in play. Cycling markets are ideal for swing trading however attempting to “trade the swing” in a trending market can be a recipe for disaster. Similarly, applying trend trading techniques during a cycling market can equally wreak havoc in your account. Cycle or trend modes can readily be identified in hindsight. But it would be useful to have an objective scientific approach to guide you as to the current market mode.
There are a number of tools already available to differentiate between cycle and trend modes. For example, measuring the trend slope over the cycle period to the amplitude of the cyclic swing is one possibility.
We begin by thinking of cycle mode in terms of frequency or its inverse, periodicity. Since the markets are fractal; daily, weekly, and intraday charts are pretty much indistinguishable when time scales are removed. Thus it is useful to think of the cycle period in terms of its bar count. For example, a 20 bar cycle using daily data corresponds to a cycle period of approximately one month.
When viewed as a waveform, slow-varying price trends constitute the waveform's low frequency components and day-to-day fluctuations (noise) constitute the high frequency components. The objective in cycle mode is to filter out the unwanted components--both low frequency trends and the high frequency noise--and retain only the range of frequencies over the desired swing period. A filter for doing this is called a bandpass filter and the range of frequencies passed is the filter's bandwidth .
Indicator Features
-Zero lag or Regular MACD/signal calculation
- Fixed or Band-pass Dominant Cycle for MACD and Signal MA period inputs
-10 different moving average options for both MACD and Signal MA calculations
-Separate Band-pass Dominant Cycle calculations for both MACD and Signal MA calculations
- Slow-to-Fast Band-pass Dominant Cycle input to tweak the ratio of MACD MA input periods as they relate to each other

Adaptive Average Vortex Index [lastguru]As a longtime fan of ADX, looking at Vortex Indicator I often wondered, where is the third line. I have rarely seen that anybody is calculating it. So, here it is: Average Vortex Index - an ADX calculated from Vortex Indicator. I interpret it similarly to the ADX indicator: higher values show stronger trend. If you discover other interpretation or have suggestions, comments are welcome.
Both VI+ and VI- lines are also drawn. As I use adaptive length calculation in my other scripts (based on the libraries I've developed and published), I have also included the possibility to have an adaptive length here, so if you hate the idea of calculating ADX from VI, you can disable that line and just look at the adaptive Vortex Indicator.
Note that as with all my oscillators, all the lines here are renormalized to -1..1 range unlike the original Vortex Indicator computation. To do that for VI+ and VI- lines, I subtract 1 from their values. It does not change the shape or the amplitude of the lines.
Adaptation algorithms are roughly subdivided in two categories: classic Length Adaptations and Cycle Estimators (they are also implemented in separate libraries), all are selected in Adaptation dropdown. Length Adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle Estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly).
VIDYA - based on VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
VIDYA-RS - based on Vitali Apirine's modification of VIDYA algorithm (he calls it Relative Strength Moving Average). The period oscillates from the Upper Bound down (fast)
Kaufman Efficiency Scaling - based on Efficiency Ratio calculation originally used in KAMA
Fractal Adaptation - based on FRAMA by John F. Ehlers
MESA MAMA Cycle - based on MESA Adaptive Moving Average by John F. Ehlers
Pearson Autocorrelation* - based on Pearson Autocorrelation Periodogram by John F. Ehlers
DFT Cycle* - based on Discrete Fourier Transform Spectrum estimator by John F. Ehlers
Phase Accumulation* - based on Dominant Cycle from Phase Accumulation by John F. Ehlers
Length Adaptation usually take two parameters: Bound From (lower bound) and To (upper bound). These are the limits for Adaptation values. Note that the Cycle Estimators marked with asterisks(*) are very computationally intensive, so the bounds should not be set much higher than 50, otherwise you may receive a timeout error (also, it does not seem to be a useful thing to do, but you may correct me if I'm wrong).
The Cycle Estimators marked with asterisks(*) also have 3 checkboxes: HP (Highpass Filter), SS (Super Smoother) and HW (Hann Window). These enable or disable their internal prefilters, which are recommended by their author - John F. Ehlers . I do not know, which combination works best, so you can experiment.
If no Adaptation is selected ( None option), you can set Length directly. If an Adaptation is selected, then Cycle multiplier can be set.
The oscillator also has the option to configure the internal smoothing function with Window setting. By default, RMA is used (like in ADX calculation). Fast Default option is using half the length for smoothing. Triangle , Hamming and Hann Window algorithms are some better smoothers suggested by John F. Ehlers.
After the oscillator a Moving Average can be applied. The following Moving Averages are included: SMA , RMA, EMA , HMA , VWMA , 2-pole Super Smoother, 3-pole Super Smoother, Filt11, Triangle Window, Hamming Window, Hann Window, Lowpass, DSSS.
Postfilter options are applied last:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic ) by John F. Ehlers
Inverse Fisher Transform - Inverse Fisher Transform
Noise Elimination Technology - a simplified Kendall correlation algorithm "Noise Elimination Technology" by John F. Ehlers
Momentum - momentum (derivative)
Except for Inverse Fisher Transform , all Postfilter algorithms can have Length parameter. If it is not specified (set to 0), then the calculated Slow MA Length is used. If Filter/MA Length is less than 2 or Postfilter Length is less than 1, they are calculated as a multiplier of the calculated oscillator length.
More information on the algorithms is given in the code for the libraries used. I am also very grateful to other TradingView community members (they are also mentioned in the library code) without whom this script would not have been possible.

Adaptive MA Difference constructor [lastguru]A complimentary indicator to my Adaptive MA constructor. It calculates the difference between the two MA lines (inspired by the Moving Average Difference (MAD) indicator by John F. Ehlers). You can then further smooth the resulting curve. The parameters and options are explained here:
The difference is normalized by dividing the difference by twice its Root mean square (RMS) over Slow MA length. Inverse Fisher Transform is then used to force the -1..1 range.
Same Postfilter options are provided as in my Adaptive Oscillator constructor:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic ) by John F. Ehlers
Inverse Fisher Transform - Inverse Fisher Transform
Noise Elimination Technology - a simplified Kendall correlation algorithm "Noise Elimination Technology" by John F. Ehlers
Momentum - momentum (derivative)
Except for Inverse Fisher Transform, all Postfilter algorithms can have Length parameter. If it is not specified (set to 0), then the calculated Slow MA Length is used.

Adaptive Oscillator constructor [lastguru]Adaptive Oscillators use the same principle as Adaptive Moving Averages. This is an experiment to separate length generation from oscillators, offering multiple alternatives to be combined. Some of the combinations are widely known, some are not. Note that all Oscillators here are normalized to -1..1 range. This indicator is based on my previously published public libraries and also serve as a usage demonstration for them. I will try to expand the collection (suggestions are welcome), however it is not meant as an encyclopaedic resource , so you are encouraged to experiment yourself: by looking on the source code of this indicator, I am sure you will see how trivial it is to use the provided libraries and expand them with your own ideas and combinations. I give no recommendation on what settings to use, but if you find some useful setting, combination or application ideas (or bugs in my code), I would be happy to read about them in the comments section.
The indicator works in three stages: Prefiltering, Length Adaptation and Oscillators.
Prefiltering is a fast smoothing to get rid of high-frequency (2, 3 or 4 bar) noise.
Adaptation algorithms are roughly subdivided in two categories: classic Length Adaptations and Cycle Estimators (they are also implemented in separate libraries), all are selected in Adaptation dropdown. Length Adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle Estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly).
Chande (Price) - based on Chande's Dynamic Momentum Index (CDMI or DYMOI), which is dynamic RSI with this length
Chande (Volume) - a variant of Chande's algorithm, where volume is used instead of price
VIDYA - based on VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
VIDYA-RS - based on Vitali Apirine's modification of VIDYA algorithm (he calls it Relative Strength Moving Average). The period oscillates from the Upper Bound down (fast)
Kaufman Efficiency Scaling - based on Efficiency Ratio calculation originally used in KAMA
Deviation Scaling - based on DSSS by John F. Ehlers
Median Average - based on Median Average Adaptive Filter by John F. Ehlers
Fractal Adaptation - based on FRAMA by John F. Ehlers
MESA MAMA Alpha - based on MESA Adaptive Moving Average by John F. Ehlers
MESA MAMA Cycle - based on MESA Adaptive Moving Average by John F. Ehlers , but unlike Alpha calculation, this adaptation estimates cycle period
Pearson Autocorrelation* - based on Pearson Autocorrelation Periodogram by John F. Ehlers
DFT Cycle* - based on Discrete Fourier Transform Spectrum estimator by John F. Ehlers
Phase Accumulation* - based on Dominant Cycle from Phase Accumulation by John F. Ehlers
Length Adaptation usually take two parameters: Bound From (lower bound) and To (upper bound). These are the limits for Adaptation values. Note that the Cycle Estimators marked with asterisks(*) are very computationally intensive, so the bounds should not be set much higher than 50, otherwise you may receive a timeout error (also, it does not seem to be a useful thing to do, but you may correct me if I'm wrong).
The Cycle Estimators marked with asterisks(*) also have 3 checkboxes: HP (Highpass Filter), SS (Super Smoother) and HW (Hann Window). These enable or disable their internal prefilters, which are recommended by their author - John F. Ehlers . I do not know, which combination works best, so you can experiment.
Chande's Adaptations also have 3 additional parameters: SD Length (lookback length of Standard deviation), Smooth (smoothing length of Standard deviation) and Power ( exponent of the length adaptation - lower is smaller variation). These are internal tweaks for the calculation.
Oscillators section offer you a choice of Oscillator algorithms:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic) by John F. Ehlers
CMO - Chande Momentum Oscillator
RSI - Relative Strength Index
Volume-scaled RSI - my own version of RSI. It scales price movements by the proportion of RMS of volume
Momentum RSI - RSI of price momentum
Rocket RSI - inspired by RocketRSI by John F. Ehlers (not an exact implementation)
MFI - Money Flow Index
LRSI - Laguerre RSI by John F. Ehlers
LRSI with Fractal Energy - a combo oscillator that uses Fractal Energy to tune LRSI gamma
Fractal Energy - Fractal Energy or Choppiness Index by E. W. Dreiss
Efficiency ratio - based on Kaufman Adaptive Moving Average calculation
DMI - Directional Movement Index (only ADX is drawn)
Fast DMI - same as DMI, but without secondary smoothing
If no Adaptation is selected (None option), you can set Length directly. If an Adaptation is selected, then Cycle multiplier can be set.
Before an Oscillator, a High Pass filter may be executed to remove cyclic components longer than the provided Highpass Length (no High Pass filter, if Highpass Length = 0). Both before and after the Oscillator a Moving Average can be applied. The following Moving Averages are included: SMA, RMA, EMA, HMA , VWMA, 2-pole Super Smoother, 3-pole Super Smoother, Filt11, Triangle Window, Hamming Window, Hann Window, Lowpass, DSSS. For more details on these Moving Averages, you can check my other Adaptive Constructor indicator:
The Oscillator output may be renormalized and postprocessed with the following Normalization algorithms:
Stochastic - Stochastic
Super Smooth Stochastic - Super Smooth Stochastic (part of MESA Stochastic) by John F. Ehlers
Inverse Fisher Transform - Inverse Fisher Transform
Noise Elimination Technology - a simplified Kendall correlation algorithm "Noise Elimination Technology" by John F. Ehlers
Except for Inverse Fisher Transform, all Normalization algorithms can have Length parameter. If it is not specified (set to 0), then the calculated Oscillator length is used.
More information on the algorithms is given in the code for the libraries used. I am also very grateful to other TradingView community members (they are also mentioned in the library code) without whom this script would not have been possible.

Adaptive MA constructor [lastguru]Adaptive Moving Averages are nothing new, however most of them use EMA as their MA of choice once the preferred smoothing length is determined. I have decided to make an experiment and separate length generation from smoothing, offering multiple alternatives to be combined. Some of the combinations are widely known, some are not. This indicator is based on my previously published public libraries and also serve as a usage demonstration for them. I will try to expand the collection (suggestions are welcome), however it is not meant as an encyclopaedic resource, so you are encouraged to experiment yourself: by looking on the source code of this indicator, I am sure you will see how trivial it is to use the provided libraries and expand them with your own ideas and combinations. I give no recommendation on what settings to use, but if you find some useful setting, combination or application ideas (or bugs in my code), I would be happy to read about them in the comments section.
The indicator works in three stages: Prefiltering, Length Adaptation and Moving Averages.
Prefiltering is a fast smoothing to get rid of high-frequency (2, 3 or 4 bar) noise.
Adaptation algorithms are roughly subdivided in two categories: classic Length Adaptations and Cycle Estimators (they are also implemented in separate libraries), all are selected in Adaptation dropdown. Length Adaptation used in the Adaptive Moving Averages and the Adaptive Oscillators try to follow price movements and accelerate/decelerate accordingly (usually quite rapidly with a huge range). Cycle Estimators, on the other hand, try to measure the cycle period of the current market, which does not reflect price movement or the rate of change (the rate of change may also differ depending on the cycle phase, but the cycle period itself usually changes slowly).
Chande (Price) - based on Chande's Dynamic Momentum Index (CDMI or DYMOI), which is dynamic RSI with this length
Chande (Volume) - a variant of Chande's algorithm, where volume is used instead of price
VIDYA - based on VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
VIDYA-RS - based on Vitali Apirine's modification of VIDYA algorithm (he calls it Relative Strength Moving Average). The period oscillates from the Upper Bound down (fast)
Kaufman Efficiency Scaling - based on Efficiency Ratio calculation originally used in KAMA
Deviation Scaling - based on DSSS by John F. Ehlers
Median Average - based on Median Average Adaptive Filter by John F. Ehlers
Fractal Adaptation - based on FRAMA by John F. Ehlers
MESA MAMA Alpha - based on MESA Adaptive Moving Average by John F. Ehlers
MESA MAMA Cycle - based on MESA Adaptive Moving Average by John F. Ehlers, but unlike Alpha calculation, this adaptation estimates cycle period
Pearson Autocorrelation* - based on Pearson Autocorrelation Periodogram by John F. Ehlers
DFT Cycle* - based on Discrete Fourier Transform Spectrum estimator by John F. Ehlers
Phase Accumulation* - based on Dominant Cycle from Phase Accumulation by John F. Ehlers
Length Adaptation usually take two parameters: Bound From (lower bound) and To (upper bound). These are the limits for Adaptation values. Note that the Cycle Estimators marked with asterisks(*) are very computationally intensive, so the bounds should not be set much higher than 50, otherwise you may receive a timeout error (also, it does not seem to be a useful thing to do, but you may correct me if I'm wrong).
The Cycle Estimators marked with asterisks(*) also have 3 checkboxes: HP (Highpass Filter), SS (Super Smoother) and HW (Hann Window). These enable or disable their internal prefilters, which are recommended by their author - John F. Ehlers. I do not know, which combination works best, so you can experiment.
Chande's Adaptations also have 3 additional parameters: SD Length (lookback length of Standard deviation), Smooth (smoothing length of Standard deviation) and Power (exponent of the length adaptation - lower is smaller variation). These are internal tweaks for the calculation.
Length Adaptaton section offer you a choice of Moving Average algorithms. Most of the Adaptations are originally used with EMA, so this is a good starting point for exploration.
SMA - Simple Moving Average
RMA - Running Moving Average
EMA - Exponential Moving Average
HMA - Hull Moving Average
VWMA - Volume Weighted Moving Average
2-pole Super Smoother - 2-pole Super Smoother by John F. Ehlers
3-pole Super Smoother - 3-pole Super Smoother by John F. Ehlers
Filt11 -a variant of 2-pole Super Smoother with error averaging for zero-lag response by John F. Ehlers
Triangle Window - Triangle Window Filter by John F. Ehlers
Hamming Window - Hamming Window Filter by John F. Ehlers
Hann Window - Hann Window Filter by John F. Ehlers
Lowpass - removes cyclic components shorter than length (Price - Highpass)
DSSS - Derivation Scaled Super Smoother by John F. Ehlers
There are two Moving Averages that are drown on the chart, so length for both needs to be selected. If no Adaptation is selected ( None option), you can set Fast Length and Slow Length directly. If an Adaptation is selected, then Cycle multiplier can be selected for Fast and Slow MA.
More information on the algorithms is given in the code for the libraries used. I am also very grateful to other TradingView community members (they are also mentioned in the library code) without whom this script would not have been possible.

Ehlers Cycle Period [CC]The Cycle Period was created by John Ehlers and this is yet another version that shows how to calculate the current cycle period which is the approximate amount of days between a current peak or valley and the next peak or valley. I would not recommend this for trading since it is more for informational use only but I would try experimenting with this output to be used with another indicator as an input length. I have included strong buy and sell signals in addition to normal ones so strong signals are darker in color and normal signals are lighter in color.
Let me know if there are any other scripts you would like to see me publish!

Ehlers Mesa Spectrum Dominant Cycle [CC]The Mesa Spectrum Dominant Cycle was created by John Ehlers and this is the foundation for many indicators he created that would later follow. This is his updated version of his original Mesa algorithm and I do not recommend this indicator as a stand alone for trading. This is more of an informational indicator that will tell you the current dominant cycle period which is the approximate period between peaks and valleys in the underlying data. I have color coded buy signals just in case with both strong and normal signals. Darker colors are strong and lighter colors are normal. Buy when the line is green and sell when it is red.
Let me know if there are any other indicators you would like to see me publish!

Ehlers Instantaneous Phase Dominant Cycle [CC]The Instantaneous Phase Dominant Cycle was created by John Ehlers (Stocks & Commodities V. 18:3 (16-27)) and this is one of many similar indicators that I will be publishing from Ehlers in the next few months that calculate the current dominant cycle period. The cycle period can be used in multiple ways but generally this means that if the stock is currently at a low then the current cycle period will tell you when the next lowest low will get hit or vice versa. This is also useful for using this cycle period as an input for other indicators to provide a very good adaptive length. Let me know how you wind up using these indicators in your daily trading. I have included the same buy and sell signals from my recent Hilbert Transform and so buy when the line turns green and sell when it turns red.
Let me know if there are any other indicators you would like to see me publish!

Dominant Cycle Adaptive MACDThis Indicator is based on classic MACD but with an exceptional smoothing.
This smoothing eliminates the noise of the classic MACD as you see in the Chart
Adaptive MACD is compiled using with two adaptive moving averages, one adaptive to the dominant cycle and the other adaptive to twice the dominant cycle. As the basic behind the MACD is the difference of two moving averages we cannot find much difference between the conventional MACD (12, 26) and the adaptive MACD. However the adaptive MACD is less prone for less whipsaws and it catches the trends very well at the same time the catches the turning points in time. The Adaptive MACD is definite one notch better than the conventional MACD.
Dominant Cycle Period is calculated using Ehler's Method {Mentioned in the code}
This is how the Adaptiveness Impacts the Price Chart
1. (12, 26 EMA) VS Adaptive Dominant Cycle EMA
2. See how the Adaptive Lengths {both FastLength and SlowLength changes with time!}
Enjoy!

[blackcat] L2 Ehlers Dominant Cycle Tuned Bandpass FilterLevel: 2
Background
John F. Ehlers introuced his Dominant Cycle Tuned Bandpass Filter Strategy in Mar, 2008.
Function
In "Measuring Cycle Periods", author John Ehlers presents a very interesting technique of measuring dominant market cycle periods by means of multiple bandpass filtering. By utilizing an approach similar to audio equalizers, the signal (here, the price series) is fed into a set of simple second-order infinite impulse response bandpass filters. Filters are tuned to 8,9,10,...,50 periods. The filter with the highest output represents the dominant cycle. A full-featured formula that implements a high-pass filter and a six-tap low-pass Fir filter on input, then 42 parallel Iir band-pass filters.
I've coded John Ehlers' filter bank to measure the dominant cycle (DC) and the sine and cosine filter components in pine v4 for TradingView, based on John Ehlers' article in this issue, "Measuring Cycle Periods." The CycleFilterDC function plots and returns the DC series and its components, so it's a trivial matter to make use of them in a trading strategy.
Based on John Ehlers' article, "Measuring Cycle Periods," he chose to implement the dominant cycle-tuned bandpass filter response to test Ehlers' suggestion to use the sine and cosine crossovers as buy and sell signals. If the sine closely follows the price pattern as suggested, and the cosine is an effective leading function of the sine, then it seems to make sense that a crossover implementation would work well (Personally, what I observed this is not so accurated as his claims).
What he discovered in his tests was that crossovers happened at frequent intervals, even when price has not moved significantly. This leads to a higher percentage of losing trades, particularly when spread, slippage, and commissions are accounted for. Nevertheless, the cosine crossover was quite effective at identifying reversals very early in many cases, so this indicator could prove quite effective when used alongside other indicators. In particular, the use of an indicator to confirm a certain level of recent volatility, as well as an indicator to confirm significant rate of change, could prove quite helpful.
Key Signal
CosineLine--> Ehlers Dominant Cycle Tuned Bandpass Filter Strategy fast line
SineLine--> Ehlers Dominant Cycle Tuned Bandpass Filter Strategy slow line
Pros and Cons
100% John F. Ehlers definition translation, even variable names are the same. This help readers who would like to use pine to read his book.
Remarks
The 72th script for Blackcat1402 John F. Ehlers Week publication.
NOTE: Although Dr. Ehlers think high of Cosine and Sine wave indicator and trading strategy, my study and trading experience indicated it did not work that well as many other oscillator indicators. However, I would like to keep the original code of Dr. Ehlers for anyone who want to make a deep dive into this kind of indicator or strategy with Cosine and Sine wave.
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.

[blackcat] L2 Ehlers DC using the Dual DifferentiatorLevel: 2
Background
John F. Ehlers introuced Measuring the Dominant Cycle using the Dual Differentiator in his "Cycle Analytics for Traders" chapter 14 on 2013.
Function
With Hilbert transformer, the first algorithm to compute the dominant cycle is called the dual differentiator. In this case, the phase angle is computed from the analytic signal as the arctangent of the ratio of the imaginary component to the real component. Further, the angular frequency is defined as the rate change of phase. We can use these facts to derive the cycle period.
Key Signal
DomCycle --> Dominant Cycle
Pros and Cons
100% John F. Ehlers definition translation, even variable names are the same. This help readers who would like to use pine to read his book.
Remarks
The 59th 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.

[blackcat] L2 Ehlers Zero Crossings Period MeasurerLevel: 2
Background
John F. Ehlers introuced Zero Crossings Period Measurer in his "Cycle Analytics for Traders" chapter 5 on 2004.
Function
The band-pass filter can be used as a relatively simple measurement of the dominant cycle. A cycle is complete when the waveform crosses zero two times from the last zero crossing. Therefore, each successive zero crossing of the indicator marks a half cycle period. We can establish the dominant cycle period as twice the spacing between successive zero crossings. When we measure the dominant cycle period this way, it is best to widen the pass band of the band-pass filter to avoid distorting the measurement simply due to the selectivity of the filter. Using an input bandwidth of 0.7 produces an octave-wide pass band. For example, if the center period of the filter is 20 and the relative bandwidth is 0.7, the bandwidth is 14. That means the pass band of the filter extends from 13-bar periods to 27-bar periods. That is, roughly an octave exists because the longest period is twice the shortest period of the pass band. It is imperative that a high-pass filter is tuned one octave below the halfbandwidth edge of the band-pass filter to ensure a nominal zero mean of the filtered output. Without a zero mean, the zero crossings can have a substantial error.
Key Signal
DC ---> dominant cycle
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 39th 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.

[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.

[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.

Ehlers Spectrum Derived Filter Bank [CC]The Spectrum Derived Filter Bank was created by John Ehlers (Stocks & Commodities V. 26:3 (16-22)) and this is technically two indicators in one. This will let you know the current cycle period which is in blue and the other indicator will let you know if you should buy the stock or not. Buy when it is green and sell when it is red.
Let me know if you would like me to publish other scripts or if you want something custom done!
Note: I'm republishing this because the original script couldn't be found in searches so this will fix that.

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.

Ehlers Discrete Fourier TransformThe Discrete Fourier Transform Indicator was written by John Ehlers and more details can be found at www.mesasoftware.com
I have color coded everything as follows: blue line is the dominant cycle, orange line is the power converted to decibels, and I have marked the other line as red if you should sell or green if you should buy
Let me know if you would like to see me write any other scripts!

Dominant Cycle Tuned Rsi BackgroundBackground version of the Dominant Cycle Tuned Rsi Background published here