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