#MAMA_v2
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This script functions as a sophisticated technical analysis tool designed to track and identify trends in financial markets. Unlike standard moving averages, which often lag behind price action, this tool utilizes complex mathematical concepts—specifically from signal processing—to adapt more dynamically to market changes.
Core Logic Overview
The indicator processes raw price data (the average of the high and low prices) through several layers of refinement to produce two distinct lines: the MAMA (MESA Adaptive Moving Average) and the FAMA (Filtered Adaptive Moving Average).
1. Signal Smoothing and Detrending
The script begins by smoothing out the price data to remove "noise." It then performs a "detrending" process, which isolates the underlying cycle of the market from its general upward or downward direction. This allows the tool to focus on the specific momentum of the price movements rather than just the general trend.
2. Cycle Detection (Frequency Analysis)
A key differentiator of this logic is how it perceives the "rhythm" of the market:
- Phase and Period Calculation: The script treats price movements as waves. It calculates the period (how often a cycle repeats) and the phase (where we are in that cycle).
- Dynamic Adaptation: By analyzing these cycles, the indicator determines how fast it should react. If the market is moving rapidly or changing direction frequently, the tool adjusts its sensitivity.
- Safety Constraints: The logic includes built-in "guardrails" to ensure the calculated periods stay within a logical range (between 6 and 50), preventing the indicator from reacting erratically to extreme outliers or impossible data points.
3. Adaptive Smoothing (The Alpha Factor)
The heart of the logic lies in the calculation of an "alpha" value. This is a dynamic multiplier that determines the weight given to new price information versus historical data:
- When the market shows significant momentum changes, the alpha increases, making the indicator react more quickly to new prices.
- When the market is stable or trending smoothly, the alpha decreases, causing the indicator to stay steady and avoid "jitter."
4. The Two Output Lines
The script produces two final visual outputs based on the adaptive calculations above:
- MAMA (Blue Line): This is the primary adaptive moving average. It follows the price closely while filtering out noise based on the cycle analysis.
- FAMA (Red Line): This is a further smoothed version of the MAMA. By taking the MAMA and applying an additional layer of filtering, it provides an even "slower" and more stable trend line.
Summary for the User
In practical terms, this script allows you to see two different types of trends simultaneously. The MAMA tells you where the immediate price momentum is heading by intelligently speeding up or slowing down its reaction, while the FAMA acts as a high-level filter to confirm the broader market direction. When these two lines interact, they provide a visual representation of whether the current market cycle is accelerating, decelerating, or changing direction.
//+------------------------------------------------------------------+
//| #MAMA.mq4 |
//| |
//| http://forex.kbpauk.ru/ |
//+------------------------------------------------------------------+
#property link "http://forex.kbpauk.ru/"
#property indicator_chart_window
#property indicator_buffers 2
#property indicator_color1 Blue
#property indicator_color2 Red
//---- input parameters
extern double FastLimit = 0.5;
extern double SlowLimit = 0.05;
//---- buffers
double FABuffer[];
double MABuffer[];
//+------------------------------------------------------------------+
//| Custom indicator initialization function |
//+------------------------------------------------------------------+
int init()
{
string short_name;
//---- indicator line
SetIndexStyle(0, DRAW_LINE, 0, 2);
SetIndexStyle(1, DRAW_LINE, 0, 2);
SetIndexBuffer(0, FABuffer);
SetIndexBuffer(1, MABuffer);
//---- name for DataWindow and indicator subwindow label
short_name = "#MAMA";
IndicatorShortName(short_name);
SetIndexLabel(0, "#FAMA");
SetIndexLabel(1, "#MAMA");
//----
SetIndexDrawBegin(0, 50);
SetIndexDrawBegin(1, 50);
//----
return(0);
}
//+------------------------------------------------------------------+
//| #MAMA |
//+------------------------------------------------------------------+
int start()
{
int i, counted_bars = IndicatorCounted();
double jI, jQ, DeltaPhase, alpha, ttime;
double Price[5], Smooth[8], Detrender[8], Q1[8], I1[8], I2[3], Q2[3];
double Re[3], Im[3], SmoothPeriod[3], Period_[3], Phase[3], MAMA[3], FAMA[3];
//----
if(Bars <= 5)
return(0);
//----
i = (Bars - counted_bars) + 50;
//----
while(i >= 0)
{
Price[1] = ((High[i] + Low[i]) / 2);
Price[2] = ((High[i+1] + Low[i+1]) / 2);
Price[3] = ((High[i+2] + Low[i+2]) / 2);
Price[4] = ((High[i+3] + Low[i+3]) / 2);
Smooth[1] = (4*Price[1] + 3*Price[2] + 2*Price[3] + Price[4]) / 10;
Detrender[1] = (0.0962*Smooth[1] + 0.5769*Smooth[3] - 0.5769*Smooth[5] -
0.0962*Smooth[7])*(0.075*Period_[2] + 0.54);
// {Compute InPhase and Quadrature components}
Q1[1] = (0.0962*Detrender[1] + 0.5769*Detrender[3] - 0.5769*Detrender[5] -
0.0962*Detrender[7])*(0.075*Period_[2] + 0.54);
I1[1] = Detrender[4];
// {Advance the phase of I1 and Q1 by 90 degrees}
jI = (0.0962*I1[1] + 0.5769*I1[3] - 0.5769*I1[5] - 0.0962*I1[7])*
(0.075*Period_[2] + 0.54);
jQ = (0.0962*Q1[1] + 0.5769*Q1[3] - 0.5769*Q1[5] - 0.0962*Q1[7])*
(0.075*Period_[2] + 0.54);
// {Phasor addition for 3 bar averaging)}
I2[1] = I1[1] - jQ;
Q2[1] = Q1[1] + jI;
// {Smooth the I and Q components before applying the discriminator}
I2[1] = 0.2*I2[1] + 0.8*I2[2];
Q2[1] = 0.2*Q2[1] + 0.8*Q2[2];
// {Homodyne Discriminator}
Re[1] = I2[1]*I2[2] + Q2[1]*Q2[2];
Im[1] = I2[1]*Q2[2] - Q2[1]*I2[2];
Re[1] = 0.2*Re[1] + 0.8*Re[2];
Im[1] = 0.2*Im[1] + 0.8*Im[2];
//----
if(Im[1] != 0 && Re[1] != 0)
Period_ [1]= 360 / MathArctan(Im[1] / Re[1]);
//----
if(Period_[1] > 1.5*Period_[2])
Period_[1] = 1.5*Period_[2];
//----
if(Period_[1] < 0.67*Period_[2])
Period_[1] = 0.67*Period_[2];
//----
if(Period_[1] < 6)
Period_[1] = 6;
//----
if(Period_[1] > 50)
Period_[1] = 50;
Period_[1] = 0.2*Period_[1] + 0.8*Period_[2];
SmoothPeriod[1] = 0.33*Period_[1] + 0.67*SmoothPeriod[2];
//----
if(I1[1] != 0)
Phase[1] = (MathArctan(Q1[1] / I1[1]));
DeltaPhase = Phase[2] - Phase[1];
//----
if(DeltaPhase < 1)
DeltaPhase = 1;
alpha = FastLimit / DeltaPhase;
//----
if(alpha < SlowLimit)
alpha = SlowLimit;
MAMA[1] = alpha*Price[1] + (1 - alpha)*MAMA[2];
FAMA[1] = 0.5*alpha*MAMA[1] + (1 - 0.5*alpha)*FAMA[2];
FABuffer[i] = MAMA[1];
MABuffer[i] = FAMA[1];
//----
Smooth[7] = Smooth[5];
Smooth[6] = Smooth[5];
Smooth[5] = Smooth[4];
Smooth[4] = Smooth[3];
Smooth[3] = Smooth[2];
Smooth[2] = Smooth[1];
//----
Detrender[7] = Detrender[6];
Detrender[6] = Detrender[5];
Detrender[5] = Detrender[4];
Detrender[4] = Detrender[3];
Detrender[3] = Detrender[2];
Detrender[2] = Detrender[1];
//----
Q1[7] = Q1[6];
Q1[6] = Q1[5];
Q1[5] = Q1[4];
Q1[4] = Q1[3];
Q1[3] = Q1[2];
Q1[2] = Q1[1];
//----
I1[7] = I1[6];
I1[6] = I1[5];
I1[5] = I1[4];
I1[4] = I1[3];
I1[3] = I1[2];
I1[2] = I1[1];
//----
Q2[2] = Q2[1];
I2[2] = I2[1];
Re[2] = Re[1];
Im[2] = Im[1];
SmoothPeriod[2] = SmoothPeriod[1];
Phase[2] = Phase[1];
Period_[2] = Period_[1];
MAMA[2] = MAMA[1];
FAMA[2] = FAMA[1];
i--;
}
return(0);
}
//+------------------------------------------------------------------+
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