357 lines
No EOL
10 KiB
MQL5
357 lines
No EOL
10 KiB
MQL5
//+------------------------------------------------------------------+
|
|
//| acf.mqh |
|
|
//| Copyright 2025, MetaQuotes Ltd. |
|
|
//| https://www.mql5.com |
|
|
//+------------------------------------------------------------------+
|
|
#property copyright "Copyright 2025, MetaQuotes Ltd."
|
|
#property link "https://www.mql5.com"
|
|
#include<VolatilityModels\np.mqh>
|
|
#include<Math\Stat\ChiSquare.mqh>
|
|
//+------------------------------------------------------------------+
|
|
//| autocorrelation function result struct |
|
|
//+------------------------------------------------------------------+
|
|
struct ACFResult
|
|
{
|
|
vector acf;
|
|
vector qstats;
|
|
vector pvalues;
|
|
matrix conf_intervals;
|
|
ACFResult(void)
|
|
{
|
|
acf = qstats = pvalues = vector::Zeros(0);
|
|
conf_intervals = matrix::Zeros(0,0);
|
|
}
|
|
ACFResult(vector& _acf, vector& _qstats, vector& _pvalues, matrix& _confintervals)
|
|
{
|
|
acf = _acf;
|
|
qstats = _qstats;
|
|
pvalues = _pvalues;
|
|
conf_intervals = _confintervals;
|
|
}
|
|
ACFResult(ACFResult& other)
|
|
{
|
|
acf = other.acf;
|
|
qstats = other.qstats;
|
|
pvalues = other.pvalues;
|
|
conf_intervals = other.conf_intervals;
|
|
}
|
|
void operator=(ACFResult& other)
|
|
{
|
|
acf = other.acf;
|
|
qstats = other.qstats;
|
|
pvalues = other.pvalues;
|
|
conf_intervals = other.conf_intervals;
|
|
}
|
|
};
|
|
//+------------------------------------------------------------------+
|
|
//| ACF function |
|
|
//+------------------------------------------------------------------+
|
|
ACFResult acf(vector& x, ulong nlags = 0, double alpha = 0.05, bool bartlett_conf=false, bool demean= true, bool adjusted = false)
|
|
{
|
|
ACFResult out;
|
|
ulong nobs = x.Size();
|
|
|
|
if(!nobs)
|
|
{
|
|
Print(__FUNCTION__, " input container is empty ");
|
|
return out;
|
|
}
|
|
|
|
if(!nlags)
|
|
nlags = MathMin(ulong(10*log10(nobs)), nobs-1);
|
|
|
|
vector avf = acovf(x,0,demean,adjusted);
|
|
|
|
if(!avf.Size())
|
|
return out;
|
|
|
|
out.acf = np::sliceVector(avf,0,long(nlags+1));
|
|
out.acf /=avf[0];
|
|
int ec = 0;
|
|
if(bartlett_conf)
|
|
{
|
|
vector varacf = vector::Ones(out.acf.Size())/double(nobs);
|
|
varacf[0] = 0.;
|
|
varacf[1] = 1./double(nobs);
|
|
vector temp = np::sliceVector(out.acf,1,out.acf.Size()-1);
|
|
vector tempsq = pow(temp,2.);
|
|
temp = np::sliceVector(varacf,2);
|
|
temp*=1.0+2.*tempsq.CumSum();
|
|
np::vectorCopy(varacf,temp,2);
|
|
|
|
vector interval = CAlglib::InvNormalCDF(1. - alpha/2.)*sqrt(varacf);
|
|
out.conf_intervals = matrix::Zeros(2,varacf.Size());
|
|
out.conf_intervals.Row(out.acf-interval,0);
|
|
out.conf_intervals.Row(out.acf+interval,1);
|
|
}
|
|
else
|
|
{
|
|
double varacf = 1./double(x.Size());
|
|
double nv = CAlglib::InvNormalCDF(1. - alpha/2.);
|
|
double interval = nv*sqrt(varacf);
|
|
out.conf_intervals = matrix::Zeros(2,out.acf.Size());
|
|
out.conf_intervals.Row(out.acf-interval,0);
|
|
out.conf_intervals.Row(out.acf+interval,1);
|
|
}
|
|
|
|
vector temp = np::sliceVector(out.acf,1);
|
|
q_stat(temp,nobs,out.qstats,out.pvalues);
|
|
|
|
return out;
|
|
}
|
|
/*//+------------------------------------------------------------------+
|
|
//|Find the next regular number greater than or equal to target. |
|
|
//+------------------------------------------------------------------+
|
|
long next_target(long target)
|
|
{
|
|
if(target<=6)
|
|
return target;
|
|
if(!(target&(target-1)))
|
|
return target;
|
|
double match = AL_POSINF;
|
|
long p5 = 1;
|
|
long p35,quotient,N,p2;
|
|
while(p5<target)
|
|
{
|
|
p35 = p5;
|
|
while(p35<target)
|
|
{
|
|
quotient =-(-target/p35);
|
|
p2=(long)pow(2,(long)bit_length(quotient-1));
|
|
N = p2*p35;
|
|
if(N == target)
|
|
return N;
|
|
else
|
|
if(double(N)<match)
|
|
match = double(N);
|
|
p35*=3;
|
|
if(p35==target)
|
|
return p35;
|
|
}
|
|
p5*=5;
|
|
if(p5==target)
|
|
return p5;
|
|
}
|
|
if(double(p5)<match)
|
|
match = double(p5);
|
|
return long(match);
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| get the number bits for an integer |
|
|
//+------------------------------------------------------------------+
|
|
ulong bit_length(long x)
|
|
{
|
|
long var = MathAbs(x);
|
|
ulong count = 1;
|
|
while(var>=2)
|
|
{
|
|
var = var/2;
|
|
++count;
|
|
}
|
|
return count;
|
|
}*/
|
|
//+------------------------------------------------------------------+
|
|
//|acovf |
|
|
//+------------------------------------------------------------------+
|
|
vector acovf(vector &in, ulong lags = 0,bool demean= true, bool adjusted = false)
|
|
{
|
|
vector xo,acov;
|
|
|
|
if(demean)
|
|
xo = in - in.Mean();
|
|
else
|
|
xo = in;
|
|
|
|
ulong n = in.Size();
|
|
|
|
ulong laglen = lags;
|
|
|
|
if(!laglen)
|
|
laglen = n-1;
|
|
else
|
|
if(lags>n-1)
|
|
{
|
|
Print(__FUNCTION__, " nlag must be smaller than ",n - 1);
|
|
return vector::Zeros(0);
|
|
}
|
|
|
|
acov = vector::Zeros(laglen+1);
|
|
|
|
acov[0] = xo.Dot(xo);
|
|
|
|
if(lags)
|
|
{
|
|
vector a,b;
|
|
for(ulong i = 0; i<laglen; ++i)
|
|
{
|
|
a = np::sliceVector(xo,long(i+1));
|
|
b = np::sliceVector(xo,0,long(xo.Size()-(i+1)));
|
|
acov[i+1] = a.Dot(b);
|
|
}
|
|
if(adjusted)
|
|
acov/=(double(n) - np::arange(laglen+1));
|
|
else
|
|
acov/=double(n);
|
|
return acov;
|
|
}
|
|
|
|
vector xi,temp,d;
|
|
|
|
if(adjusted)
|
|
{
|
|
xi = np::arange(n,1.);
|
|
d = vector::Zeros((xi.Size()*2)-1);
|
|
np::vectorCopy(d,xi,0,xi.Size());
|
|
temp = np::sliceVector(xi,0,xi.Size()-1);
|
|
np::reverseVector(temp);
|
|
np::vectorCopy(d,temp,xi.Size());
|
|
}
|
|
else
|
|
d = double(n)*vector::Ones(2*n-1);
|
|
/*if(fft)
|
|
{
|
|
ulong nobs = xo.Size();
|
|
n = ulong(next_target(long(2*nobs+1)));
|
|
CRowComplex Frf;
|
|
CRowDouble inx = xo;
|
|
CFastFourierTransform::FFTR1D(inx,int(nobs),Frf);
|
|
vectorc frf = Frf.ToVector();
|
|
frf = frf*frf.Conjugate();
|
|
Frf = frf;
|
|
CFastFourierTransform::FFTR1DInv(Frf,Frf.Size(),inx);
|
|
temp = inx.ToVector();
|
|
temp = np::sliceVector(temp,0,nobs);
|
|
acov = temp/np::sliceVector(d,long(nobs-1));
|
|
}
|
|
else
|
|
{*/
|
|
acov = xo.Correlate(xo,VECTOR_CONVOLVE_FULL);
|
|
acov = np::sliceVector(acov,long(n-1))/np::sliceVector(d,long(n-1));
|
|
//}
|
|
|
|
if(lags)
|
|
return np::sliceVector(acov,0,long(laglen+1));
|
|
|
|
return acov;
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//|LjungBox q statistic |
|
|
//+------------------------------------------------------------------+
|
|
bool q_stat(vector& x, ulong nvars, vector& out_stats, vector& out_pvals)
|
|
{
|
|
vector r = np::arange(x.Size(),1.) ;
|
|
r = (1.0/(double(nvars) - r))*pow(x,2.);
|
|
out_stats = double(nvars)*double(nvars+2)*r.CumSum();
|
|
out_pvals = out_stats;
|
|
r = np::arange(x.Size(),1.);
|
|
int error_note = 0;
|
|
for(ulong i = 0; i<out_pvals.Size(); ++i)
|
|
out_pvals[i] = 1. - MathCumulativeDistributionChiSquare(out_stats[i],r[i],error_note);
|
|
if(error_note)
|
|
return false;
|
|
return true;
|
|
}
|
|
//+------------------------------------------------------------------+
|
|
//| plot the ACF |
|
|
//+------------------------------------------------------------------+
|
|
|
|
void plot_acf(ACFResult& acf,long chart_id = 0,int x_coordinate = 0, int y_coordinate = 0, int subwindow = 0,int width = 600, int height = 400,string plot_name = NULL, int fontsize = 15, long viewtimeseconds = 30, bool showchart=true )
|
|
{
|
|
if(!acf.acf.Size())
|
|
{
|
|
Print(__FUNCTION__, " Results object is empty ");
|
|
return;
|
|
}
|
|
|
|
if(StringLen(plot_name)<1)
|
|
plot_name = "Autocorrelation Function";
|
|
|
|
CGraphic* graph = new CGraphic();
|
|
//---
|
|
if(!chart_id)
|
|
chart_id = ChartID();
|
|
//---
|
|
ChartRedraw(chart_id);
|
|
//---
|
|
ChartSetInteger(chart_id, CHART_SHOW, showchart);
|
|
//---
|
|
if(!graph.Create(chart_id,plot_name,subwindow,x_coordinate,y_coordinate,width,height))
|
|
{
|
|
delete graph;
|
|
Print(__FUNCTION__," Failed to Create graphical object on the Main chart Err ", GetLastError());
|
|
return;;
|
|
}
|
|
//---
|
|
double x[], y[];
|
|
ArrayResize(x,(int)acf.acf.Size());
|
|
ArrayResize(y,(int)acf.acf.Size());
|
|
//---
|
|
int ncurves = 4;
|
|
//---
|
|
ENUM_CURVE_TYPE ctype = WRONG_VALUE;
|
|
//---
|
|
for(int i=0; i<ncurves; ++i)
|
|
{
|
|
for(uint j = 0; j<x.Size(); ++j)
|
|
{
|
|
if(i<2)
|
|
{
|
|
x[j] = double(j);
|
|
y[j] = acf.acf[j];
|
|
ctype = (i==0)?CURVE_HISTOGRAM:CURVE_POINTS;
|
|
}
|
|
else
|
|
{
|
|
ctype = CURVE_LINES;
|
|
if(i == 2)
|
|
y[j] = (acf.conf_intervals[1,j]-acf.conf_intervals[0,j])/2.;
|
|
else
|
|
y[j] = (acf.conf_intervals[0,j]-acf.conf_intervals[1,j])/2.;
|
|
|
|
}
|
|
}
|
|
//---
|
|
CCurve* newcurve = graph.CurveAdd(x, y,ctype,NULL);
|
|
//---
|
|
switch(ctype)
|
|
{
|
|
case CURVE_HISTOGRAM:
|
|
newcurve.Color(ColorToARGB(clrBlue));
|
|
newcurve.HistogramWidth(2);
|
|
break;
|
|
case CURVE_POINTS:
|
|
newcurve.PointsFill(true);
|
|
newcurve.PointsColor(ColorToARGB(clrBlue));
|
|
newcurve.Color(ColorToARGB(clrBlue));
|
|
newcurve.PointsSize(8);
|
|
break;
|
|
default:
|
|
newcurve.Color(ColorToARGB(clrRed));
|
|
newcurve.LinesStyle(STYLE_DOT);
|
|
break;
|
|
}
|
|
}
|
|
//---
|
|
graph.BackgroundMain(plot_name);
|
|
graph.BackgroundMainSize(fontsize+5);
|
|
graph.BackgroundMainColor(ColorToARGB(clrBlack));
|
|
//---
|
|
graph.HistoryNameWidth(0);
|
|
graph.HistorySymbolSize(0);
|
|
graph.HistoryNameSize(0);
|
|
//---
|
|
graph.XAxis().Name("Lags");
|
|
graph.XAxis().NameSize(fontsize);
|
|
//---
|
|
graph.YAxis().Name("Correlation Coefficient");
|
|
graph.YAxis().NameSize(fontsize);
|
|
//---
|
|
graph.CurvePlotAll();
|
|
graph.Update();
|
|
//---
|
|
Sleep(int(viewtimeseconds)*1000);
|
|
graph.Destroy();
|
|
delete graph;
|
|
ChartRedraw(chart_id);
|
|
//---
|
|
} |