MESA Adaptive Moving Average (MAMA)

[DaveSkender]

Community discussion about MESA Adaptive Moving Average (MAMA)

[DaveSkender]

I think John Ehlers is just making up words in his formula for this indicator. Remember, you'll need to determine the quadrature before the homodyne discriminator! 😮 Serious math in this one ... he is definitely a genius to be able to create this one. I now understand why he nicknamed it "mother of adaptive moving averages".

[JosueNina]

Hi Dave,

I'm currently working on creating my own MAMA indicator and testing it with different libraries. While comparing your indicator with the MAMA from the ta-lib library, I noticed that the values are slightly different. Could you explain if this is due to using a simple average for the first 6 values? I found the following code in your implementation:

sumPr += pr[i];

if (i == 5)
{
    r.Mama = (sumPr / 6d).NaN2Null();
    r.Fama = r.Mama;
}

Additionally, I noticed that you use radians for the period calculation, which I think is correct:

pd[i] = im[i] != 0 && re[i] != 0
                    ? 2 * Math.PI / Math.Atan(im[i] / re[i])
                    : 0d;

And then you use degrees for the phase calculation:
ph[i] = (i1[i] != 0) ? Math.Atan(q1[i] / i1[i]) * 180 / Math.PI : 0;

Could you explain why this distinction is made?

Thanks!

[DaveSkender]

Regarding SMA initialization. Since this indicator uses a smoothing technique, FAMA and MAMA values have to be initialized. John Ehler's whitepaper implies that these initialize as 0 values. I usually do honor the original author's approach; however, in this case, using SMA is more aligned with how most moving averages are initialized to reduce early period errors.

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Using the SMA initialization value here instead of 0 allows the early periods to have a smaller convergence errors, even though they do end up converging synchronously from the 100-350+ periods.¹

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In reality, this is what initial values look like, comparing SMA (gray line) vs 0 (orange line) initialization values to steady-state converged MAMA values (blue line).

Footnotes

1. This convergence analysis uses different quotes, price scale (potentially confusing). ↩

[DaveSkender]

I'm still looking into the radian vs. degrees concern; though still believe this is just a way to get everything into the correct units for each value used in the final calculations.

[JosueNina]

That makes sense. As for the second part, I've seen many implementations doing 360 / arctan(), which is incorrect. In your case, 2 * pi / arctan() makes sense since both are in radians. Also, the phase should be in degrees

, which your code also handles correctly.

I think that answers all my questions. Thanks again for the quick response!

[DaveSkender]

Mostly depends on the code language. .NET returns radians from math.Atan() while others may be in degrees.