Adaptive Trend Lines [MAMA and FAMA]Updated my previous algo on the Adaptive Trend lines, however I have added new functionalities and sorted out the settings.
You can now switch between normalized and non-normalized settings, the colors have also been updated and look much better.
The MAMA and FAMA
These indicators was originally developed by John F. Ehlers (Stocks & Commodities V. 19:10: MESA Adaptive Moving Averages). Everget wrote the initial functions for these in pine script. I have simply normalized the indicators and chosen to use the Laplace transformation instead of the hilbert transformation
How the Indicator Works:
The indicator employs a series of complex calculations, but we'll break it down into key steps to understand its functionality:
LaplaceTransform: Calculates the Laplace distribution for the given src input. The Laplace distribution is a continuous probability distribution, also known as the double exponential distribution. I use this because of the assymetrical return profile
MESA Period: The indicator calculates a MESA period, which represents the dominant cycle length in the price data. This period is continuously adjusted to adapt to market changes.
InPhase and Quadrature Components: The InPhase and Quadrature components are derived from the Hilbert Transform output. These components represent different aspects of the price's cyclical behavior.
Homodyne Discriminator: The Homodyne Discriminator is a phase-sensitive technique used to determine the phase and amplitude of a signal. It helps in detecting trend changes.
Alpha Calculation: Alpha represents the adaptive factor that adjusts the sensitivity of the indicator. It is based on the MESA period and the phase of the InPhase component. Alpha helps in dynamically adjusting the indicator's responsiveness to changes in market conditions.
MAMA and FAMA Calculation: The MAMA and FAMA values are calculated using the adaptive factor (alpha) and the input price data. These values are essentially adaptive moving averages that aim to capture the current trend more effectively than traditional moving averages.
But Omar, why would anyone want to use this?
The MAMA and FAMA lines offer benefits:
The indicator offers a distinct advantage over conventional moving averages due to its adaptive nature, which allows it to adjust to changing market conditions. This adaptability ensures that investors can stay on the right side of the trend, as the indicator becomes more responsive during trending periods and less sensitive in choppy or sideways markets.
One of the key strengths of this indicator lies in its ability to identify trends effectively by combining the MESA and MAMA techniques. By doing so, it efficiently filters out market noise, making it highly valuable for trend-following strategies. Investors can rely on this feature to gain clearer insights into the prevailing trends and make well-informed trading decisions.
This indicator is primarily suppoest to be used on the big timeframes to see which trend is prevailing, however I am not against someone using it on a timeframe below the 1D, just be careful if you are using this for modern portfolio theory, this is not suppoest to be a mid-term component, but rather a long term component that works well with proper use of detrended fluctuation analysis.
Dont hesitate to ask me if you have any questions
Again, I want to give credit to Everget and ChartPrime!
Code explanation as required by House Rules:
fastLimit = input.float(title='Fast Limit', step=0.01, defval=0.01, group = "Indicator Settings")
slowLimit = input.float(title='Slow Limit', step=0.01, defval=0.08, group = "Indicator Settings")
src = input(title='Source', defval=close, group = "Indicator Settings")
input.float: Used to create input fields for the user to set the fastLimit and slowLimit values.
input: General function to get user inputs, like the data source (close price) used for calculations.
norm_period = input.int(3, 'Normalization Period', 1, group = "Normalized Settings")
norm = input.bool(defval = true, title = "Use normalization", group = "Normalized Settings")
input.int: Creates an input field for the normalization period.
input.bool: Allows the user to toggle normalization on or off.
Color settings in the code:
col_up = input.color(#22ab94, group = "Color Settings")
col_dn = input.color(#f7525f, group = "Color Settings")
Constants and functions
var float PI = math.pi
laplace(src) =>
(0.5) * math.exp(-math.abs(src))
_computeComponent(src, mesaPeriodMult) =>
out = laplace(src) * mesaPeriodMult
out
_smoothComponent(src) =>
out = 0.2 * src + 0.8 * nz(src )
out
math.pi: Represents the mathematical constant π (pi).
laplace: A function that applies the Laplace transform to the source data.
_computeComponent: Computes a component of the data using the Laplace transform.
_smoothComponent: Smooths data by averaging the current value with the previous one (nz function is used to handle null values).
Alpha function:
_computeAlpha(src, fastLimit, slowLimit) =>
mesaPeriod = 0.0
mesaPeriodMult = 0.075 * nz(mesaPeriod ) + 0.54
...
alpha = math.max(fastLimit / deltaPhase, slowLimit)
out = alpha
out
_computeAlpha: Calculates the adaptive alpha value based on the fastLimit and slowLimit. This value is crucial for determining the MAMA and FAMA lines.
Calculating MAMA and FAMA:
mama = 0.0
mama := alpha * src + (1 - alpha) * nz(mama )
fama = 0.0
fama := alpha2 * mama + (1 - alpha2) * nz(fama )
Normalization:
lowest = ta.lowest(mama_fama_diff, norm_period)
highest = ta.highest(mama_fama_diff, norm_period)
normalized = (mama_fama_diff - lowest) / (highest - lowest) - 0.5
ta.lowest and ta.highest: Find the lowest and highest values of mama_fama_diff over the normalization period.
The oscillator is normalized to a range, making it easier to compare over different periods.
And finally, the plotting:
plot(norm == true ? normalized : na, style=plot.style_columns, color=col_wn, title = "mama_fama_diff Oscillator Normalized")
plot(norm == false ? mama_fama_diff : na, style=plot.style_columns, color=col_wnS, title = "mama_fama_diff Oscillator")
Example of Normalized settings:
Example for setup:
Try to make sure the lower timeframe follows the higher timeframe if you take a trade based on this indicator!
MESA адаптивная скользящая средняя (MAMA)
GKD-C Mother of AMA (MAMA) [Loxx]Giga Kaleidoscope Mother of AMA (MAMA) is a Confirmation module included in Loxx's "Giga Kaleidoscope Modularized Trading System".
█ Giga Kaleidoscope Modularized Trading System
What is Loxx's "Giga Kaleidoscope Modularized Trading System"?
The Giga Kaleidoscope Modularized Trading System is a trading system built on the philosophy of the NNFX (No Nonsense Forex) algorithmic trading.
What is an NNFX algorithmic trading strategy?
The NNFX algorithm is built on the principles of trend, momentum, and volatility. There are six core components in the NNFX trading algorithm:
1. Volatility - price volatility; e.g., Average True Range, True Range Double, Close-to-Close, etc.
2. Baseline - a moving average to identify price trend
3. Confirmation 1 - a technical indicator used to identify trends
4. Confirmation 2 - a technical indicator used to identify trends
5. Continuation - a technical indicator used to identify trends
6. Volatility/Volume - a technical indicator used to identify volatility/volume breakouts/breakdown
7. Exit - a technical indicator used to determine when a trend is exhausted
How does Loxx's GKD (Giga Kaleidoscope Modularized Trading System) implement the NNFX algorithm outlined above?
Loxx's GKD v1.0 system has five types of modules (indicators/strategies). These modules are:
1. GKD-BT - Backtesting module (Volatility, Number 1 in the NNFX algorithm)
2. GKD-B - Baseline module (Baseline and Volatility/Volume, Numbers 1 and 2 in the NNFX algorithm)
3. GKD-C - Confirmation 1/2 and Continuation module (Confirmation 1/2 and Continuation, Numbers 3, 4, and 5 in the NNFX algorithm)
4. GKD-V - Volatility/Volume module (Confirmation 1/2, Number 6 in the NNFX algorithm)
5. GKD-E - Exit module (Exit, Number 7 in the NNFX algorithm)
(additional module types will added in future releases)
Each module interacts with every module by passing data between modules. Data is passed between each module as described below:
GKD-B => GKD-V => GKD-C(1) => GKD-C(2) => GKD-C(Continuation) => GKD-E => GKD-BT
That is, the Baseline indicator passes its data to Volatility/Volume. The Volatility/Volume indicator passes its values to the Confirmation 1 indicator. The Confirmation 1 indicator passes its values to the Confirmation 2 indicator. The Confirmation 2 indicator passes its values to the Continuation indicator. The Continuation indicator passes its values to the Exit indicator, and finally, the Exit indicator passes its values to the Backtest strategy.
This chaining of indicators requires that each module conform to Loxx's GKD protocol, therefore allowing for the testing of every possible combination of technical indicators that make up the six components of the NNFX algorithm.
What does the application of the GKD trading system look like?
Example trading system:
Backtest: Strategy with 1-3 take profits, trailing stop loss, multiple types of PnL volatility, and 2 backtesting styles
Baseline: Hull Moving Average
Volatility/Volume: Volatility Ratio as shown on the chart above
Confirmation 1: Mother of AMA (MAMA) as shown on the chart above
Confirmation 2: Williams Percent Range
Continuation: Fisher Transform
Exit: Rex Oscillator
Each GKD indicator is denoted with a module identifier of either: GKD-BT, GKD-B, GKD-C, GKD-V, or GKD-E. This allows traders to understand to which module each indicator belongs and where each indicator fits into the GKD protocol chain.
Giga Kaleidoscope Modularized Trading System Signals (based on the NNFX algorithm)
Standard Entry
1. GKD-C Confirmation 1 Signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
6. GKD-C Confirmation 1 signal was less than 7 candles prior
Continuation Entry
1. Standard Entry, Baseline Entry, or Pullback; entry triggered previously
2. GKD-B Baseline hasn't crossed since entry signal trigger
3. GKD-C Confirmation Continuation Indicator signals
4. GKD-C Confirmation 1 agrees
5. GKD-B Baseline agrees
6. GKD-C Confirmation 2 agrees
1-Candle Rule Standard Entry
1. GKD-C Confirmation 1 signal
2. GKD-B Baseline agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
Next Candle:
1. Price retraced (Long: close < close or Short: close > close )
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume agrees
1-Candle Rule Baseline Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
4. GKD-C Confirmation 1 signal was less than 7 candles prior
Next Candle:
1. Price retraced (Long: close < close or Short: close > close )
2. GKD-B Baseline agrees
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume Agrees
PullBack Entry
1. GKD-B Baseline signal
2. GKD-C Confirmation 1 agrees
3. Price is beyond 1.0x Volatility of Baseline
Next Candle:
1. Price is within a range of 0.2x Volatility and 1.0x Volatility of the Goldie Locks Mean
3. GKD-C Confirmation 1 agrees
4. GKD-C Confirmation 2 agrees
5. GKD-V Volatility/Volume Agrees
█ Mother of AMA (MAMA)
What is Mother of AMA (MAMA)?
The Ehlers Mother of Adaptive Moving Average (MAMA) is a technical analysis indicator developed by John F. Ehlers. It is a type of moving average that uses a combination of exponential moving averages (EMAs) and adaptive filtering to provide a smoothed price trend line with reduced lag and noise.
The MAMA indicator is composed of two lines: the fast MAMA line and the slow FAMA line. The fast MAMA line is designed to be more responsive to short-term price movements, while the slow FAMA line is designed to be more responsive to longer-term trends. The MAMA lines are constructed using an adaptive algorithm that adjusts to market volatility and changes in trend, making it more effective in volatile markets.
The Ehlers MAMA indicator is used by traders to identify trend reversals, and to generate buy and sell signals. When the fast MAMA line crosses above the slow FAMA line, it is considered a bullish signal, and when the fast MAMA line crosses below the slow FAMA line, it is considered a bearish signal. Additionally, the MAMA indicator can be used in combination with other technical indicators to confirm trading signals and improve trading accuracy.
The FAMA component of the MAMA (Mother of Adaptive Moving Average) is the slowest of the two lines that make up the MAMA indicator. It is designed to respond more slowly to changes in price than the fast MAMA line, and is calculated as an exponential moving average of the fast MAMA line.
The FAMA component is adaptive, meaning that it adjusts to changes in market volatility and trend. In volatile markets, the FAMA line will adjust more quickly to changes in price, while in less volatile markets, it will adjust more slowly. This makes the FAMA line more effective at identifying longer-term trends and reducing lag.
The combination of the fast MAMA line and the slow FAMA line in the MAMA indicator provides traders with a reliable trend-following tool that responds quickly to changes in price while remaining stable enough to avoid false signals. When the fast MAMA line crosses above the slow FAMA line, it is a signal to buy, and when the fast MAMA line crosses below the slow FAMA line, it is a signal to sell. By using the MAMA indicator in conjunction with other technical analysis tools, traders can improve their trading accuracy and make more informed trading decisions.
The white line is the FAMA and the colored line is the MAMA. Crosses of the MAMA over the FAMA are longs, crosses under are shorts.
Requirements
Inputs
Confirmation 1 and Solo Confirmation: GKD-V Volatility / Volume indicator
Confirmation 2: GKD-C Confirmation indicator
Outputs
Confirmation 2 and Solo Confirmation: GKD-E Exit indicator
Confirmation 1: GKD-C Confirmation indicator
Continuation: GKD-E Exit indicator
Additional features will be added in future releases.
IchiMAMA (Experimental)Goichi Hosoda's "Ichimoku Kinkō Hyō" is a widely used Trend Following indicator and can be defined as a "system" rather than an indicator.
Published in the late 1960's, consisting of 5 lines.
TenkanSen (Conversion Line) = of the last 9 bars
KijunSen (Base Line) = of the last 26 bars
SenkouSpanA (Leading Span A) = Average of Tenkan&KijunSen shifted -> 26 bars
SenkouSpanB (Leading Span B) = of the last 52 bars
ChikouSpan (Lagging Span) = Price shifted <- 26 bars
On the other hand, Mesa Adaptive Moving Average developed by John Ehlers around early 2000's shows similarities with Hosoda's Tenkan and KijunSen using a different calculation method. For futher info: www.mesasoftware.com
I find MAMA superior to TenkanSen and KijunSen in terms of crossing signals.
Ichimoku:
Thus, decided to replace TenkanSen and KijunSen of regular Ichimoku with MAMA&FAMA of Ehlers and calculated SenkouSpanA accordingly. SenkouSpanB and ChikouSpan stays the same as per Ichimoku's logic. (Periods are 30 by default for cryptocurrencies. If stocks then 26)
IchiMAMA:
This is purely experimental and educational. Hope you'll like it :)
I'd like to thank @everget for MAMA&FAMA
and @KivancOzbilgic for Ichimoku Kinkō Hyō and Volume Based Colored Bars
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 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.
DominantCycleCollection of Dominant Cycle estimators. 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). This collection may become encyclopaedic, so if you have any working cycle estimator, drop me a line in the comments below. Suggestions are welcome. Currently included estimators are based on the work of John F. Ehlers
mamaPeriod(src, dynLow, dynHigh) MESA Adaptation - MAMA Cycle
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
Returns: Calculated period
Based on MESA Adaptive Moving Average by John F. Ehlers
Performs Hilbert Transform Homodyne Discriminator cycle measurement
Unlike MAMA Alpha function (in LengthAdaptation library), this does not compute phase rate of change
Introduced in the September 2001 issue of Stocks and Commodities
Inspired by the @everget implementation:
Inspired by the @anoojpatel implementation:
paPeriod(src, dynLow, dynHigh, preHP, preSS, preHP) Pearson Autocorrelation
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
preHP : Use High Pass prefilter (default)
preSS : Use Super Smoother prefilter (default)
preHP : Use Hann Windowing prefilter
Returns: Calculated period
Based on Pearson Autocorrelation Periodogram by John F. Ehlers
Introduced in the September 2016 issue of Stocks and Commodities
Inspired by the @blackcat1402 implementation:
Inspired by the @rumpypumpydumpy implementation:
Corrected many errors, and made small speed optimizations, so this could be the best implementation to date (still slow, though, so may revisit in future)
High Pass and Super Smoother prefilters are used in the original implementation
dftPeriod(src, dynLow, dynHigh, preHP, preSS, preHP) Discrete Fourier Transform
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
preHP : Use High Pass prefilter (default)
preSS : Use Super Smoother prefilter (default)
preHP : Use Hann Windowing prefilter
Returns: Calculated period
Based on Spectrum from Discrete Fourier Transform by John F. Ehlers
Inspired by the @blackcat1402 implementation:
High Pass, Super Smoother and Hann Windowing prefilters are used in the original implementation
phasePeriod(src, dynLow, dynHigh, preHP, preSS, preHP) Phase Accumulation
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
preHP : Use High Pass prefilter (default)
preSS : Use Super Smoother prefilter (default)
preHP : Use Hamm Windowing prefilter
Returns: Calculated period
Based on Dominant Cycle from Phase Accumulation by John F. Ehlers
High Pass and Super Smoother prefilters are used in the original implementation
doAdapt(type, src, len, dynLow, dynHigh, chandeSDLen, chandeSmooth, chandePower, preHP, preSS, preHP) Execute a particular Length Adaptation or Dominant Cycle Estimator from the list
Parameters:
type : Length Adaptation or Dominant Cycle Estimator type to use
src : Series to use
len : Reference lookback length
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
chandeSDLen : Lookback length of Standard deviation for Chande's Dynamic Length
chandeSmooth : Smoothing length of Standard deviation for Chande's Dynamic Length
chandePower : Exponent of the length adaptation for Chande's Dynamic Length (lower is smaller variation)
preHP : Use High Pass prefilter for the Estimators that support it (default)
preSS : Use Super Smoother prefilter for the Estimators that support it (default)
preHP : Use Hann Windowing prefilter for the Estimators that support it
Returns: Calculated period (float, not limited)
doEstimate(type, src, dynLow, dynHigh, preHP, preSS, preHP) Execute a particular Dominant Cycle Estimator from the list
Parameters:
type : Dominant Cycle Estimator type to use
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
preHP : Use High Pass prefilter for the Estimators that support it (default)
preSS : Use Super Smoother prefilter for the Estimators that support it (default)
preHP : Use Hann Windowing prefilter for the Estimators that support it
Returns: Calculated period (float, not limited)
LengthAdaptationCollection of dynamic length adaptation algorithms. Mostly from various Adaptive Moving Averages (they are usually just EMA otherwise). Now you can combine Adaptations with any other Moving Averages or Oscillators (see my other libraries), to get something like Deviation Scaled RSI or Fractal Adaptive VWMA. This collection is not encyclopaedic. Suggestions are welcome.
chande(src, len, sdlen, smooth, power) Chande's Dynamic Length
Parameters:
src : Series to use
len : Reference lookback length
sdlen : Lookback length of Standard deviation
smooth : Smoothing length of Standard deviation
power : Exponent of the length adaptation (lower is smaller variation)
Returns: Calculated period
Taken from Chande's Dynamic Momentum Index (CDMI or DYMOI), which is dynamic RSI with this length
Original default power value is 1, but I use 0.5
A variant of this algorithm is also included, where volume is used instead of price
vidya(src, len, dynLow) Variable Index Dynamic Average Indicator (VIDYA)
Parameters:
src : Series to use
len : Reference lookback length
dynLow : Lower bound for the dynamic length
Returns: Calculated period
Standard VIDYA algorithm. The period oscillates from the Lower Bound up (slow)
I took the adaptation part, as it is just an EMA otherwise
vidyaRS(src, len, dynHigh) Relative Strength Dynamic Length - VIDYA RS
Parameters:
src : Series to use
len : Reference lookback length
dynHigh : Upper bound for the dynamic length
Returns: Calculated period
Based on Vitali Apirine's modification (Stocks and Commodities, January 2022) of VIDYA algorithm. The period oscillates from the Upper Bound down (fast)
I took the adaptation part, as it is just an EMA otherwise
kaufman(src, len, dynLow, dynHigh) Kaufman Efficiency Scaling
Parameters:
src : Series to use
len : Reference lookback length
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
Returns: Calculated period
Based on Efficiency Ratio calculation orifinally used in Kaufman Adaptive Moving Average developed by Perry J. Kaufman
I took the adaptation part, as it is just an EMA otherwise
ds(src, len) Deviation Scaling
Parameters:
src : Series to use
len : Reference lookback length
Returns: Calculated period
Based on Derivation Scaled Super Smoother (DSSS) by John F. Ehlers
Originally used with Super Smoother
RMS originally has 50 bar lookback. Changed to 4x length for better flexibility. Could be wrong.
maa(src, len, threshold) Median Average Adaptation
Parameters:
src : Series to use
len : Reference lookback length
threshold : Adjustment threshold (lower is smaller length, default: 0.002, min: 0.0001)
Returns: Calculated period
Based on Median Average Adaptive Filter by John F. Ehlers
Discovered and implemented by @cheatcountry:
I took the adaptation part, as it is just an EMA otherwise
fra(len, fc, sc) Fractal Adaptation
Parameters:
len : Reference lookback length
fc : Fast constant (default: 1)
sc : Slow constant (default: 200)
Returns: Calculated period
Based on FRAMA by John F. Ehlers
Modified to allow lower and upper bounds by an unknown author
I took the adaptation part, as it is just an EMA otherwise
mama(src, dynLow, dynHigh) MESA Adaptation - MAMA Alpha
Parameters:
src : Series to use
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
Returns: Calculated period
Based on MESA Adaptive Moving Average by John F. Ehlers
Introduced in the September 2001 issue of Stocks and Commodities
Inspired by the @everget implementation:
I took the adaptation part, as it is just an EMA otherwise
doAdapt(type, src, len, dynLow, dynHigh, chandeSDLen, chandeSmooth, chandePower) Execute a particular Length Adaptation from the list
Parameters:
type : Length Adaptation type to use
src : Series to use
len : Reference lookback length
dynLow : Lower bound for the dynamic length
dynHigh : Upper bound for the dynamic length
chandeSDLen : Lookback length of Standard deviation for Chande's Dynamic Length
chandeSmooth : Smoothing length of Standard deviation for Chande's Dynamic Length
chandePower : Exponent of the length adaptation for Chande's Dynamic Length (lower is smaller variation)
Returns: Calculated period (float, not limited)
doMA(type, src, len) MA wrapper on wrapper: if DSSS is selected, calculate it here
Parameters:
type : MA type to use
src : Series to use
len : Filtering length
Returns: Filtered series
Demonstration of a combined indicator: Deviation Scaled Super Smoother
TEMA/MAMA CrossThis is a strategy based on the TEMA and Ehler's MAMA moving averages. Crosses of the fast and slow TEMA are commonly used for entry and exit strategies. The Ehler's Mesa Adaptive Moving Average is a trend-following price indicator that uses a Hilbert Transform. Having plotted both TEMA and eMAMA side-by-side for some time, I noticed a pattern where the fastTEMA crossed over the eFAMA (eFAMA is the Ehler's MAMA following/slow MA) prior to a price increase. This is a strategy to test that observation.
The strategy (at present) only does long entries. It enters long when the fastTEMA crosses up over the (slow) eFAMA. It uses a traditional exit when the fastTEMA crosses below the slowTEMA. I have tested this on several tokens on 1hr charts using a fastTEMA length of 13. Play with it on different charts and different lengths to see how it works for you.
[blackcat] L2 Ehlers MAMALevel: 2
Background
John F. Ehlers introuced MESA Adaptive Moving Average-a.k.a "MAMA" in his "Rocket Science for Traders" chapter 17. Forgive the whimsy of the name Dr. Ehlers attached to this unique indicator, but with that name he is sure you will always remember it, like KAMA and VIDYA.
Function
blackcat L2 Ehlers MESA Adaptive Moving Average-a.k.a "MAMA" is used to follow trend. The concept of MAMA is to relate the phase rate of change to the EMA alpha, thus making the EMA adaptive. The cycle phase goes from 0 through 360 degrees in each cycle. The phase is continuous, but is usually drawn with the snap back to 0 degrees as the beginning of each cycle. Thus the phase rate of change is 360 degrees per cycle. The shorter the cycle, the faster the phase rate of change. For example, a 36-bar cycle has a phase rate of change of 10 degrees per bar, while a 10-bar cycle has a rate of change of 36 degrees per bar. The cycle periods tend to be longer when the market is in a Trend Mode.
The cycle phase is computed from the arctangent of the ratio of the Quadrature component to the Inphase component. Dr. Ehlers obtain the phase rate of change values by taking the difference of successive phase measurements. The arctangent function only measures phase over a half cycle, from -90 degrees to +90 degrees. Since the phase measurement snaps back every half cycle, a huge negative rate change of phase every half cycle results from the computation of the rate change of phase. Measured negative rate changes of phase can also occur when the market is in a Trend Mode. Any negative rate change of phase is theoretically impossible because phase must advance as time increases. Dr. Ehlers therefore limit all rate change of phase to be no less than unity.
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
alpha ---> coefficient
MAMA ---> MESA Adaptive Moving Average-a.k.a "MAMA"
FAMA ---> slow line of MAMA
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 13th 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.
RK's 07 ∴ Moving Average Ribbon with Momentum Adjusted by DGTHello folks!
In my search for new ways to get faster and better market responses, I found this brilliant Indicator here on Trading View.
I rewrite all the code with my own functions and styles.
So... This is my adaptation to excellent script "Momentum adjusted Moving Average by DGT" from the user dgtrd
In dgtrd's words: "A brand new Moving Average, calculated using Momentum, Acceleration and Probability (Psychological Effect).
Momentum adjusted Moving Average( MaMA ) is an indicator that measures Price Action by taking into consideration not only Price movements but also its Momentum, Acceleration and Probability.
MaMA , provides faster responses comparing to the regular Moving Average"
The original post is here: 👇
T∴F∴A∴
Rodrigo Kazuma
Ehlers Mother Of Adaptive Moving Averages [CC]The Mother Of Adaptive Moving Averages was created by John Ehlers (Rocket Science For Traders pgs 182-183) and this is definitely my favorite Ehlers moving average script. This works as a trend indicator and a typical moving average. When the mama is above the fama then the stock is in an uptrend and vice versa. Of course it is also good when the price is above the fama and mama lines. Buy when the indicator line is green and sell when it is red.
Let me know if there are other indicator scripts you would like to see me publish or if you want something custom done!
MAMA FAMA KAMA.. chameleon 🎵
Uses Kaufmann's Efficiency Ratio to generate adaptive inputs for Ehler's MAMA/FAMA. Alphas from the Hilbert transform are then used in place for the KAMA calculation.
Original MAMA/FAMA by everget : link
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If you find it useful please consider a tip/donation :
BTC - 3BMEXEDyWJ58eXUEALYPadbn1wwWKmf6sA
Profitable MAMA & FAMA CrossoverIntroduction
The MESA Adaptive Moving Average (MAMA) was originally presented by John F. Ehlers. By design, it is a special kind of Exponential Moving Average with self-adjusting alpha. Its adaptation is based on the rate change of phase as measured by the Homodyne Discriminator and the alpha parameter is allowed to range between a maximum and minimum value (Fast Limit and Slow Limit).
Key Point: Ehlers suggested the maximum value to be 0.5 and the minimum to be 0.05 .
The variable alpha is computed as the Fast Limit divided by the phase rate of change. If the phase rate of change is large, the variable alpha is bounded at the SlowLimit. Then, this alpha is used to compute MAMA and FAMA (Following Adaptive Moving Average).
Should we rely on Ehlers' suggestions if we want to achieve the best result with MAMA & FAMA crossover system?
Well, he is a good specialist and widely recognized author, I respect him, but the answer is no and you can see results on the chart.
What is our goal?
We want to find the best configuration for MAMA & FAMA Crossover. To achieve that we need to analyze the MAMA's alpha parameter or, more specific, the bounds for this parameter, Fast and Slow Limits.
What is this tool?
This tool is a performance optimizer that uses decision tree-based algorithm under the hood to find the most profitable settings for the MAMA & FAMA Crossover. It analyzes a bunch of different Fast Limits (between 0.01 to 0.8 with step of 0.1 ) and Slow Limits (between 0.01 to 0.6 with step of 0.1 ) and backtests each combination across the entire history of an instrument. If the more profitable parameters were found, the indicator will switch its values to the found ones immediately.
So, instead of manually selecting and testing parameters just apply this indicator to your chart and
relax - the algorithm will find the best parameters for you
Alerts
It has a special alert that notifies when the more profitable settings were detected.
NOTE: It does not change what has already been plotted.
NOTE 2: This is not a strategy, but an algorithmic optimizer.
Reference: www.mesasoftware.com
MAMA & FAMA Crossover can be found here:
MESA Adaptive Moving AverageIntro
One of Ehlers most well-known indicators! I've seen many variations of this on TradingView, however, none seem to be true to the original released by Ehlers himself.
I've taken it upon myself to simply translate the MAMA into Pinescript, instead of re-writing like some others have done.
You can use it as a very effective & adaptive moving average with other signals or
as a standalone signal.
In the case that you're going to use it for signals and not simple technical trading (non-quantitative),
I've also added a threshold parameter to filter out weak signals.
My MAMA indicator is different from others in very simple ways - I don't use the nz() command, which sets all "Not a Number" values to 0. In others' scripts, you immediately load the indicator with several 0 values,
causing a slight lag in future calculations since this code is recursive (refers to previous values it generated).
In my version, I simply wait until the script has access to all the bar data it needs, instead of instantly performing calculations and
setting erroneous values to 0. In this case, we start with the correct values (or closer to correct).
If you want to compare this indicator the current most popular MAMA by LazyBear, you'll notice it often gives buy and sell crosses one bar earlier than theirs.
Setting Parameters
Source - the data series to perform calculations on. (Initially, Ehlers himself favored hl/2, but conceded that there isn't empirical benefit over close.)
Fast Limit - controls how quickly the MAMA will "ratchet up" fast price action. (Higher values are faster)
Slow Limit - controls how closely the FAMA will follow the MAMA. (Again, higher is faster. You typically want the FAMA to be slower though.)
Crossover Threshold - simple error thresholding to limit the number of weak trade signals. (Lower means lower tolerance)
Show Crosses? - show/hide the arrows at moving average crosses
MAMA by EHLERSMESA Adaptive Moving Average aka: Mother of Adaptive Moving Averages:
The MESA Adaptive Moving Average ( MAMA ) adapts to price movement in an
entirely new and unique way. The adapation is based on the rate change of phase as
measured by the Hilbert Transform Discriminator I have previously described.1
The advantage of this method of adaptation is that it features a fast attack average and a
slow decay average so that composite average rapidly ratchets behind price changes
and holds the average value until the next ratchet occurs. The action of MAMA is
shown in Figure 1. Since the average fallback is slow I can build trading systems that
are virtually free of whipsaw trades.
For detailed information of MAMA: (creators' PDF document)
www.mesasoftware.com
Long condition: when MAMA Crosses over FAMA (Following Adaptive Moving Average )
Short condition: when FAMA Crosses over MAMA
(Personally modified LazyBear's version which was originally calculated in degrees instead of radian by applying explanations in the MESA pdf document.http://www.mesasoftware.com/papers/MAMA.pdf)
Creator: John EHLERS
Trader Set - Volume CandleThis is a candlestick system but not on price. These candles are drawn based on the volume movement. This is one of those professional charting systems that big industries use every day. Remember, the key to find what smart money is doing, is always VOLUME. Any new way that you can track new aspects of volume will help determining what the market will do, BEFORE it starts doing it !
There are total of Seven moving averages that you can ...:
1- Set their period separately
2- Set their type separately
3- Turn on/off separately
The averaging types that are supported, remember you have options PER moving average :
- SMA
- EMA
- RMA
- WMA
- HMA
- KAMA
- MAMA
- FAMA
This script IS FOR SALE , you can buy it with crypto currencies, or webmoney or perfect money. THE PRICE is 55$. for life time license.
You can find all the crypto wallet addresses plus webmoney and perfect money accounts in the link below. Please send the correct amount PLUS the transaction fee. After the transaction is confirmed, contact me with the info of the transaction for granting access.
AَِDDRESSES FOR WALLETS : justpaste.it
Ehlers MESA Adaptive Moving Averages (MAMA & FAMA)Ehlers MESA Adaptive Moving Averages (MAMA & FAMA) script.
These indicators was originally developed by John F. Ehlers (Stocks & Commodities V. 19:10: MESA Adaptive Moving Averages).
Adaptive MAs (MAMA, FAMA, KAMA)Adaptive moving averages a.k.a volatility-weighted moving averages are great tools for filtering out whipsawed trades as well as protecting the traders from premature exits when using stoploss. Adaptive moving averages are constructed in such a way that:
1) as volatility increases the sensitivity of the moving averages decreases, distancing the moving averages from price.
2) as volatility subsides, the sensitivity of the adaptive moving average starts to increase, drawing it closer to price action.
References:
stockcharts.com
www.mesasoftware.com
Find me on Twitter .
Ehlers MESA Adaptive Moving Average [LazyBear with ekoronin fix]Mama/Fama with ekronin's fix: www.tradingview.com
Fractal Dimension Adaptive Moving Average (D-AMA)etfhq.com
Overall the D-AMA produced results that were near identical to that of the FRAMA but the D-AMA is a slightly faster average.
It is very difficult to pick between the FRAMA and the D-AMA but becuase the FRAMA offers a slightly longer trade duration it the best Moving Average we have tested so far.
Ehlers MESA Adaptive Moving Average [LazyBear]Another one to add to Ehlers collection.
The MESA Adaptive Moving Average (MAMA) adapts to price movement based on the rate of change of phase as measured by the Hilbert Transform Discriminator. This method features a fast attack average and a slow decay average so that composite average rapidly ratchets behind price changes and holds the average value until the next ratchet occurs. Consider FAMA (Following AMA) as the signal.
Here are some of the options:
Fill MAMA/FAMA region (ribbon mode):
Mark Crossovers:
The above options (along with the bar colors) allow this to be used as a standalone system.
BTW, John Ehlers calls MAMA, "Mother of all Adaptive Moving Averages", lemme know what you think :)
More info:
- MESA Adaptive Moving Average, Stocks and Commodities Magazine, August 2001
- MAMA: www.mesasoftware.com
List of my public indicators: bit.ly
List of my app-store indicators: blog.tradingview.com
