Ehlers Dominant Cycle

/_SECTION_BEGIN("Unnamed 13");
// Dominant Cycle

SetBarsRequired( 10000, 0 );

// USER DEFINED PARAMS

Price = ( High + Low ) / 2;

// FORMULA

// initialize variables

Smooth = Detrender = I1 = Q1 = jI = jQ = I2 = Q2 = Re = Im = Period = SmoothPeriod = 0;

// calculate dominant cycle period

for ( i = 6; i < BarCount; i++ )

{

// smooth price data with 4-bar WMA

Smooth[i] = ( 4 * Price[i] + 3 * Price[i-1] + 2 * Price[i-2] + Price[i-3] ) / 10;

// compute amplitude correction

AmpCorr[i] = 0.075 * Period[i-1] + 0.54;

// compute detrended price data and Quadrature component with 7-bar Hilbert Transform

Detrender[i] = ( 0.0962 * Smooth[i] + 0.5769 * Smooth[i-2] - 0.5769 * Smooth[i-4] - 0.0962 * Smooth[i-6] ) * AmpCorr[i];

Q1[i] = ( 0.0962 * Detrender[i] + 0.5769 * Detrender[i-2] - 0.5769 * Detrender[i-4] - 0.0962 * Detrender[i-6] ) * AmpCorr[i];

// compute InPhase component by referencing center bar of Hilbert Transformer ( 3 bars ago )

I1[i] = Detrender[i-3];

// advance the phase of I1 and Q1 by 90 degrees with 7-bar Hilbert Transform

jI[i] = ( 0.0962 * I1[i] + 0.5769 * I1[i-2] - 0.5769 * I1[i-4] - 0.0962 * I1[i-6] ) * AmpCorr[i];

jQ[i] = ( 0.0962 * Q1[i] + 0.5769 * Q1[i-2] - 0.5769 * Q1[i-4] - 0.0962 * Q1[i-6] ) * AmpCorr[i];

// perform Phasor addition for 3-bar averaging

I2[i] = I1[i] - jQ[i];

Q2[i] = Q1[i] + jI[i];

// smooth the I and Q components

I2[i] = 0.2 * I2[i] + 0.8 * I2[i-1];

Q2[i] = 0.2 * Q2[i] + 0.8 * Q2[i-1];

// apply the Homodyne Discriminator

Re[i] = I2[i] * I2[i-1] + Q2[i] * Q2[i-1];

Im[i] = I2[i] * Q2[i-1] - Q2[i] * I2[i-1];

// smooth the Re and Im components

Re[i] = 0.2 * Re[i] + 0.8 * Re[i-1];

Im[i] = 0.2 * Im[i] + 0.8 * Im[i-1];

// compute Dominant Cycle period

if ( Im[i] != 0 AND Re[i] != 0 )

Period[i] = 360 / atan( Im[i] / Re[i] );

// limit ROC of the cycle period to +/- 50% of previous cycle period

if ( Period[i] > 1.5 * Period[i-1] )

Period[i] = 1.5 * Period[i-1];

if ( Period[i] < 0.67 * Period[i-1] )

Period[i] = 0.67 * Period[i-1];

// limit the cycle period to be > 6 or < 50

if ( Period[i] < 6 )

Period[i] = 6;

if ( Period[i] > 50 )

Period[i] = 50;

// smooth the cycle period

Period[i] = 0.2 * Period[i] + 0.8 * Period[i-1];

SmoothPeriod[i] = 0.33 * Period[i] + 0.67 * SmoothPeriod[i-1];

}

Plot( SmoothPeriod, "Dominant Cycle", colorWhite, styleLine|styleOwnScale );

Plot( Re, "Re", colorLightBlue, styleLine|styleOwnScale );

Plot( Im, "Im", colorRed, styleLine|styleOwnScale );

Plot( Im/Re, "Im/Re", colorDarkGreen, styleLine|styleOwnScale );

Plot( atan(Im/Re), "atan(Im/Re)", colorBrightGreen, styleLine|styleOwnScale );

Plot( Period, "Period", colorOrange, styleLine|styleOwnScale );


_SECTION_END();

GraphXSpace = 5;