MAMA

The MAMA or Mother Of Adaptive Moving Averages was authored by John Ehlers. The MAMA uses the current price, three previous prices, several feedback sequences, a few math functions and factors, and some more feedback for its final calculation. A signal line, called the FAMA which is derived from the MAMA, is also given. The user may change the input (midpoint) and the fast and slow factors. This indicator’s definition is further expressed in the condensed code given in the calculation below.

See also article by John Ehlers

How To Trade Using MAMA

If the MAMA crosses below the FAMA a sell signal will be generated. Conversely, if the MAMA crosses above the FAMA a buy signal will be given.

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Calculation

//input = price, user defined, default is midpoint
//fast = user defined, default is .5
//slow = user defined, default is .05
//prev = previous, index = current bar number

prevPrice1 = price[index-1];
prevPrice2 = price[index-2];
prevPrice3 = price[index-3];
prevPrd = period[index-1];
smooth = (4 * price + 3 * prevPrice1 + 2 * prevPrice2 + prevPrice3)  / 10;
prevS2 = smooth[index-2];
prevS4 = smooth[index-4];
prevS6 = smooth[index-6];
det = (.0962 * smooth + .5769 * prevS2 - .5769 * prevS4 - .0962 * prevS6) * (.075 * prevPrd + .54);
prevD2 = det[index-2];
prevD3 = det[index-3];
prevD4 = det[index-4];
prevD6 = det[index-6];
q1 = (.0962 * det + .5769 * prevD2 - .5769 * prevD4 - .0962 * prevD6) * (.075 * prevPrd + .54);
i1 = prevD3;
prevQ1x2 = q1[index-2];
prevQ1x4 = q1[index-4];
prevQ1x6 = q1[index-6];
prevI1x2 = i1[index-2];
prevI1x4 = i1[index-4];
prevI1x6 = i1[index-6];
j1 = (.0962 * i1 + .5769 * prevI1x2 - .5769 * prevI1x4 - .0962 * prevI1x6) * (.075 * prevPrd + .54);
jq = (.0962 * q1 + .5769 * prevQ1x2 - .5769 * prevQ1x4 - .0962 * prevQ1x6) * (.075 * prevPrd + .54);
i2 = i1 - jq;
q2 = q1 + j1;
prevI2 = i2[index-1];
prevQ2 = q2[index-1];
i2 = .2*i2 + .8 * prevI2;
q2 = .2*q2 + .8 * prevQ2;
re = i2*prevI2 + q2 * prevQ2;
im = i2*prevQ2 - q2 * prevI2;
prevRe = re[index-1];
prevIm = im[index-1];
re = .2*re + .8 * prevRe;
im = .2*im + .8 * prevIm;
if (im != 0 AND re != 0) period = 360/Math.atan(im/re);
if (period moreThan 1.5 * prevPrd) period = 1.5 * prevPrd;
if (period lessThan .67 * prevPrd) period = .67 * prevPrd;
if (period  50) period = 50;
period = .2 * period + .8 * prevPrd;
prevSprd = sprd[index-1];
sPrd = .33 * period + .67 * prevSprd;
if (i1 != 0) phase = Math.atan(q1/i1);
prevPhase = phase[index-1];
deltaPhase = prevPhase - phase;
if (deltaPhase lessThan 1) deltaPhase = 1;
alpha = fast / deltaPhase;
if (alpha lessThan slow) alpha = slow;
prevMama = mama[index-1];
prevFama = fama[index-1];
Plot1: mama = alpha * price + (1 - alpha) * prevMama;
Plot2: fama = .5 * alpha * mama + (1 - .5 * alpha) * prevFama;
 //Signals
buy = crossedAbove(MAMA, FAMA);
sell =crossedBelow(MAMA, FAMA);