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.
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To follow Ehlers original work line 72 should be:
Phase := I1 != 0 ? 180/pi * atan(Q1 / I1) : Phase
for lines 74, 75 and 76 were written for DeltaPhase in degrees not radians.
blackcat1402
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@sal157011, thanks, but every triangular function in pine use radians. This is the reason why I translated everything again from Ehlers and guarantee every details in radians.
you can check sin, cos, atan function manual in pine manual, there are always note that like "The arc tangent of a value; the returned angle is in the range (-Pi/2, Pi/2)."
This is the biggest difference when tranlating Ehlers works into pine because original work used Easy Language which used degree while Pine uses radians.
Can you agree with me on this ? Correct me if my understand on triangular difference is wrong and appreciate your remarks all the time :D
sal157011
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@blackcat1402, Your understanding on triangular difference is 100% correct. The problem is that line 74 was intended by Ehlers to limit the rate of change to be not less than unity, see page 180 paragraph 2 of his book, the unit he is talking about is one degree not one radian. So, or we convert the Phase in line 72 to degrees and let the lines 74, 75 and 76 unchanged, which is the easiest solution, or we let the Phase in line 72 in radians and the lines 74, 75 and 76 must be changed but I don't know how.
Phase := I1 != 0 ? 180/pi * atan(Q1 / I1) : Phase
for lines 74, 75 and 76 were written for DeltaPhase in degrees not radians.