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# "BB-MACD" Created by KelvinHand Using Ehlers Periodogram for the Dominant Cycle

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Hi

I would like to Plot the "BB-MACD" Created by KelvinHand

for a Variable Time Period Dominant Cycle as

calculated by "Ehlers Autocorrelation Periodogram" code below

I have only able to plot the "BB-MACD" Created by KelvinHand

using the fixed time period of the last value of "Ehlers Autocorrelation Periodogram"

Hoping that you can help

Best regards

Derek

//////////////////////////////////////////////////////

```//Ehlers Autocorrelation Periodogram for Amibroker (AFL)

/*
Autocorrelation Periodogram
2013 John F. Ehlers
*/

SetBarsRequired(sbrAll);

LPeriod = Param("Low-pass Period", 10, 3, 20);
HPeriod = Param("High-pass Period", 48, 22, 80);
IsPlotHeatMap = ParamToggle("Show HeatMap?", "No|Yes", 1);
IsPlotDominantCycle = ParamToggle("Show Dom. Cycle?", "No|Yes");

pi=3.1415926;

function RoofingFilter(lpPeriod, hpPeriod)
{
alpha1 = (cos(0.707*2*pi / hpPeriod) + sin(0.707*2*pi / hpPeriod) - 1) / cos(0.707*2*pi / hpPeriod);
a1 = exp(-1.414*pi / lpPeriod);
b1 = 2*a1*cos(1.414*pi / lpPeriod);
c2 = b1;
c3 = -a1*a1;
c1 = 1 - c2 - c3;

HP = Close;
Filt = HP;

for(i = 2; i < BarCount; i++)
{
HP[i] = ((1 - alpha1 / 2)^2)*(Close[i] - 2*Close[i-1] + Close[i-2]) + 2*(1 - alpha1)*HP[i-1] - ((1 - alpha1)^2)*HP[i-2];
Filt[i] = c1*(HP[i] + HP[i-1]) / 2 + c2*Filt[i-1] + c3*Filt[i-2];
}

return Filt;
}

function AGC(lowerCutoff, higherCutoff, acceptableSlope)
{
factor = 0;
accSlope = -acceptableSlope;	//acceptableSlope = 1.5 dB
halfLC = lowerCutoff / 2;
halfHC = higherCutoff / 2;
ratio = 10^(accSlope/20);
if(halfHC - halfLC > 0)
factor = ratio^(1/(halfHC - halfLC));
return factor;
}

function AutocorrelationPeriodogram(data, isHeatMap, isDomCyc)
{
avgLength = 3;
dominantCycle = 0;

//Pearson correlation for each value of lag
for(lag = 0; lag <= 48; lag++)
{
//Set the average length as M
M = avgLength;
if(avgLength == 0)
M = lag;
//Initialize correlation sums
Sx = 0;
Sy = 0;
Sxx = 0;
Syy = 0;
Sxy = 0;
//Advance samples of both data streams and sum Pearson components
for(count = 0; count <= M-1; count++)
{
X = Ref(data, -count);
Y = Ref(data, -(lag + count));
Sx += X;
Sy += Y;
Sxx += X^2;
Syy += Y^2;
Sxy += X*Y;
}
var1 = (M*Sxx - Sx^2)*(M*Syy - Sy^2);
VarSet("corr" + lag, IIf(var1 > 0, (M*Sxy - Sx*Sy)/sqrt(var1), 0));	//Compute correlation for each value of lag
//VarSet("corrScale" + lag, IIf(var1 > 0, 0.5*((M*Sxy - Sx*Sy)/sqrt(var1) + 1), 0));	//Scale each correlation to range between 0 and 1
}

/*//Plot as a Heatmap (for scale each correlation to range between 0 and 1)
for(period = 3; period <= 48; period++)
{
corr = VarGet("corrScale" + period);
Red = IIf(corr > 0.5, 255*(2 - 2*corr), 255);
Green = IIf(corr > 0.5, 255, 2*255*corr);
PlotOHLC( period-1, period-1, period, period, "", ColorRGB( Red, Green, 0 ), styleCloud | styleNoLabel);
}*/

/*
The DFT is accomplished by correlating the autocorrelation at each value of lag with the cosine and sine of each period of interest.
The sum of the squares of each of these values represents the relative power at each period.
*/
for(period = 10; period <= 48; period++)
{
cosinePart = 0;
sinePart = 0;

for(n = 3; n <= 48; n++)
{
cosinePart += VarGet("corr" + n)*cos(2*pi*n / period);
sinePart += VarGet("corr" + n)*sin(2*pi*n / period);
}
VarSet("sqSum" + period, cosinePart^2 + sinePart^2);
}

//EMA is used to smooth the power measurement at each period
for(period = 10; period <= 48; period++)
VarSet("r" + period, AMA((VarGet("sqSum" + period))^2, 0.2));

//Find Maximum Power Level for Normalization
K = AGC(10, 48, 1.5);
for(period = 10; period <= 48; period++)
{
if(period == 10)
VarSet("maxPwr", 0);
VarSet("maxPwr", IIf(VarGet("r" + period) > VarGet("maxPwr"), K*VarGet("r" + period), VarGet("maxPwr")));
}

//Normalization power
for(period = 10; period <= 48; period++)
VarSet("pwr" + period, VarGet("r" + period)/VarGet("maxPwr"));

//Compute the dominant cycle using the CG of the spectrum
Spx = 0;
Sp = 0;
for(period = 10; period <= 48; period++)
{
Spx += IIf(VarGet("pwr" + period) >= 0.5,  period*VarGet("pwr" + period), 0);
Sp += IIf(VarGet("pwr" + period) >= 0.5, VarGet("pwr" + period), 0);
}
dominantCycle = IIf(Sp != 0, Spx / Sp, 0);
dominantCycle =(dominantCycle);

if(isHeatMap)
{
//Plot as a Heatmap
for(period = 10; period <= 48; period++)
{
pwr = VarGet("pwr" + period);
Red = IIf(pwr > 0.5, 255, 2*255*pwr);
Green = IIf(pwr > 0.5, 255*(2*pwr - 1), 0);
PlotOHLC( period-1, period-1, period, period, "", ColorRGB( Red, Green, 0 ), styleCloud | styleNoLabel, Null, Null, 0, 0);
}
}

if(isDomCyc)
Plot(LastValue(dominantCycle,1), "Dominant Cycle", colorBlue, styleThick, Null, Null, 0, 1);

pds=LastValue(dominantCycle,1);

//"BB-MACD")    Created by KelvinHand

SetChartBkColor( ParamColor("background",colorBlack) );
A1=EMA(C,pds/2)-EMA(C,pds);
BBtop=BBandTop(A1,10,1);
BBbot=BBandBot(A1,10,1);
Color=IIf(a1<0 AND a1>Ref(a1,-1), colorLime,IIf(a1>0 AND a1>Ref(a1,-1),colorBrightGreen,IIf(a1>0 AND a1<Ref(a1,-1),colorCustom12,colorRed)));

Plot(a1,"MACD",color,styleThick+styleLine);
Plot(BBtop,"BBtop",colorWhite,styleDashed);
Plot(BBbot,"BBbot",colorWhite,styleDashed);
Plot(0,"",colorWhite,1);

AddColumn(round(dominantCycle), " DominantCycle", 2.0 ,  colorRed, colorLightYellow,50) ;

return dominantCycle;

}

filtData = RoofingFilter(LPeriod, HPeriod);
AutocorrelationPeriodogram(filtData, IsPlotHeatMap, IsPlotDominantCycle);

```

]

##### Share on other sites

HI

See attached PNG screenshot file of BB-MACD for Dax Sept 02

Best regards

Derk

BB-MACD Created by KelvinHand.txt

##### Share on other sites

Link below for the code of John F. Ehlers Autocorrelation Periodogram for Amibroker (AFL)

with thanks to : < Ilya > for the translation to Amibroker (AFL)

Derek

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