Fourier Transform for traders
Employing Fourier Transform in Amibroker AFL allows traders to decompose price movements into their frequency components, aiding in identifying cyclic patterns. Integrating Amibroker data feed facilitates real-time analysis, enabling traders to capitalize on recurring market cycles for strategic trading decisions.
/_SECTION_BEGIN("Fourier Transform For Traders");
PI = 3.1415926;
Data = (H+L)/2;
// detrending ( high-pass filter )
HFPeriods = Param("HP filter cutoff", 40, 20, 100 );
alpha1 = ( 1-sin(2*pi/HFPeriods) ) / cos( 2 * pi / HFPeriods );
HP = AMA2( Data - Ref( Data, -1 ), 0.5 * ( 1 + alpha1 ), alpha1 );
// 6-tap low-pass FIR filter
CleanedData = ( HP + 2 * Ref( HP, -1 ) + 3 * Ref( HP, -2 ) +
3 * Ref( HP, -3 ) + 2 * Ref( HP, -4 ) + Ref( HP, -5 ) )/12;
// Discrete Fourier Transform
WindowSize = Param("Window Size", 50, 20, 100 );
Maxpwr = 0;
x = BarIndex();
for( period = 8; period <= WindowSize; period++ )
{
tx = 2 * pi * x / period;
cosinepart = Sum( CleanedData * cos( tx ), WindowSize );
sinepart = Sum( CleanedData * sin( tx ), WindowSize );
pwr = cosinepart ^ 2 + sinepart ^ 2;
Maxpwr = Max( Maxpwr, pwr );
VarSet( "pwr"+period, pwr );
}
// Normalize and convert to decibels
for( period = 8; period <= WindowSize; period++ )
{
pwr = VarGet("pwr"+period);
db = -10 * log10( 0.01 / ( 1 - 0.99 * pwr / Maxpwr ) );
db = Min( db, 20 ); // 'saturate' at -20db
VarSet( "db"+period, db );
}
Title = Name() + " HiRes DFT : ";
// Plot Heat Map ( Spectrogram )
// and find dominant cycle
DcNum = DcDenom = 0;
for( k = 8; k <= WindowSize; k++ )
{
db = VarGet("db"+k);
// convert dB to color
Red = IIf( db > 10, 255 * ( 2 - db/10 ), 255 );
Green = IIf( db <= 10, 255 * ( 1 - db/10 ), 0 );
PlotOHLC( k, k, k-1, k-1, "",
ColorRGB( Red, Green, 0 ), styleCloud | styleNoLabel);
if( SelectedValue( db ) <= 5 )
Title = Title + k + " = " + StrFormat("%.2lf",-db) + "dB, ";
// dominant cycle calcs
DcNum = DcNum + (db < 3 ) * k * ( 3 - db );
DcDenom = DcDenom + ( db < 3 ) * ( 3 - db );
}
if( ParamToggle("Show Dom. Cycle?", "No|Yes" ) )
{
DominantCycle = DcNum / DcDenom;
Plot( DominantCycle, "Dominant Cycle", colorBlue );
Title = Title + "{{VALUES}}";
}
GraphZOrder = 1;
_SECTION_END();