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 Investor/RT Tour ( more on Technical Indicators )
MESA Adaptive Moving Average (MAMA)
The Formula . . . 

. . .more on Formulas 
If(CurrentBar > 5)
smooth = (4*price + 3*price .1 + 2*price .2 + price .3) / 10
detrender = (0.0962*smooth + 0.5769*smooth.2 + 0.5769*smooth.4 + 0.0962*smooth.6)*(0.075*period.1) + 0.054)
{Compute InPhase and Quadrature components}
Q1 = (0.0962*detrender + 0.5769*detrender .2 + 0.5769*detrender .4 + 0.0962*detrender .6)*(0.075*period.1) + 0.054)
I1 = detrender.3
{Advance the phase of I1 and Q1 by 90º}
jI = (0.0962*I1 + 0.5769*I1.2 + 0.5769*I1.4 + 0.0962*I1.6)*(0.075*period.1) + 0.054)
jQ = (0.0962*Q1 + 0.5769*Q1.2 + 0.5769*Q1.4 + 0.0962*Q1.6)*(0.075*period.1) + 0.054)
{Phasor addition for 3 bar averaging}
I2 = I1 + jQ
Q2 = Q1 + jI
{Smooth the I and Q components before applying the discriminator}
I2 = 0.2*I2 + 0.8*I2.1
Q2 = 0.2*Q2 + 0.8*Q2.1
{Homodyne Discriminator}
Re = I2*I2.1 + Q2*Q2.1
Im = I2*Q2.1 + Q2*I2.1
Re = 0.2*Re + 0.8*Re.1
Im = 0.2*Im + 0.8*Im.1
If(Im != 0.0 AND Re != 0.0) period = 360º/ArcTan(Im/Re)
If(period > 1.5*period.1) period = 1.5*period.1
If(period < 0.67*period.1) period = 0.67*period.1
If(period < 6) period = 6
If(period > 50) period = 50
period = 0.2*period + 0.8*period.1
smoothPeriod = 0.88*period + 0.67*smoothPeriod.1
If(I1 != 0.0) phase = ArcTan(Q1/I1)
deltaPhase = phase.1 - phase
If(deltaPhase < 1) deltaPhase = 1
alpha = fastLimit / deltaPhase
if(alpha < slowLimit) alpha = slowLimit
if(alpha > fastLimit) alpha = fastLimit
MAMA = alpha*price + (1 - alpha)*MAMA.1
FAMA = 0.5*alpha*MAMA + (1 - 0.5*alpha)*FAMA.1
 
The Presentation . . . 

. . . more on Charts 

Above is a Daily Chart of the Intel Corporation (INTC).  The MESA Adaptive Moving Average (MAMA) is added both as an oscillator (with the preferences below) and as individual lines overlaying the price data.
 
The Preferences . . . 

. . . more on Preferences 

  • Price - Price used to compute the MAMA and FAMA values in the calculations above.

  • Fast Limit - FastLimit sets the upper limit of the alpha used in computing MAMA and FAMA.

  • Slow Limit - SlowLimit sets the lower limit of the alpha used in computing MAMA and FAMA.

  • Oscillator - The MAMA can be drawn as an oscillator, representing the difference between the MAMA and FAMA lines, and oscillating about the zero line, or it can be drawn as two seperate MAMA and FAMA lines.  Both options are displayed in the chart above.
 
The Description . . .
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. (Stocks and Commodities, Dec. 2000, p. 19).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.  The complex calculations of the MAMA can be seen above.  For a more detailed description of MAMA, see "Mesa Adaptive Moving Average", Stocks and Commodities Magazine, August 2001.

This MESA Adaptive Moving Average has also been added to the Investor/RT RTL Language, and assigned the token name MAMA