【解説】【MQL5 community】 AR Extrapolator of Price : ARモデル(自己回帰モデル : 時系列解析で良く使用されている手法)を用いて、予想を表示するIndicator。
ARモデルとは次で与えられる.
x[n] = -Sum(a[i]*x[n - i], i = 1..p)
ただし x[n] は予測する価格変動、x[n-p]..x[n-1]は過去の価格, a[1]..a[p] はこのモデルの係数で, pは次元を表している. 特にここでは、Burg Methodでパラメーターフィッティングを行う.
//+--------------------------------------------------------------------------------------+
//| AR_Extrapolator_of_Price.mq5 |
//| Copyright gpwr |
//+--------------------------------------------------------------------------------------+
#property copyright "gpwr"
#property version "1.00"
#property description "Extrapolation of open prices by autoregressive (AR) model"
#property indicator_chart_window
#property indicator_buffers 2
#property indicator_plots 2
//--- future model outputs
#property indicator_label1 "Modeled future"
#property indicator_type1 DRAW_LINE
#property indicator_color1 Red
#property indicator_style1 STYLE_SOLID
#property indicator_width1 1
//--- past model outputs
#property indicator_label2 "Modeled past"
#property indicator_type2 DRAW_LINE
#property indicator_color2 Blue
#property indicator_style2 STYLE_SOLID
#property indicator_width2 1
//===================================== INPUTS ===========================================
input bool UseDiff =false; // Use price difference
input int Ncoef =150; // # of model coefficients (model order)
input int Nfut =100; // # of future bars
input double kPast =3; // # of past bars in increments of Ncoef (must be >=1)
// Global variables
int Npast,dN;
// Indicator buffers
double ym[],xm[];
// Custom indicator initialization function ---------------------------------------------+
void OnInit()
{
// Initialize global variables
Npast=kPast*Ncoef;
if(UseDiff) dN=1;
else dN=0;
// Map indicator buffers
ArraySetAsSeries(xm,true);
ArraySetAsSeries(ym,true);
SetIndexBuffer(0,ym,INDICATOR_DATA);
SetIndexBuffer(1,xm,INDICATOR_DATA);
IndicatorSetInteger(INDICATOR_DIGITS,_Digits);
IndicatorSetString(INDICATOR_SHORTNAME,"AR("+string(Npast)+","+string(Ncoef)+")");
PlotIndexSetInteger(0,PLOT_SHIFT,Nfut);
}
//====================================== MAIN ============================================
int OnCalculate(const int rates_total,
const int prev_calculated,
const datetime& Time[],
const double& Open[],
const double& High[],
const double& Low[],
const double& Close[],
const long& tick_volume[],
const long& volume[],
const int& spread[])
{
// Check for insufficient data
if(rates_total＜Npast+1)
{
Print("Error: not enough bars in history!");
return(0);
}
// Initialize indicator buffers to EMPTY_VALUE
ArrayInitialize(xm,EMPTY_VALUE);
ArrayInitialize(ym,EMPTY_VALUE);
// Make all prices available
MqlRates rates[];
ArraySetAsSeries(rates,true);
if(CopyRates(NULL,0,0,Npast+1,rates)＜=0) return(0);
// Main cycle ---------------------------------------------------------------------------+
// Prepare model inputs
double x[];
ArrayResize(x,Npast);
for(int i=0;i＜Npast;i++) x[Npast-1-i]=rates[i].open-rates[i+1].open*dN;
// Solve for AR model coefficients
double a[];
ArrayResize(a,Ncoef+1);
Burg(x,Npast,Ncoef,a);
// Calculate past and future predictions by fitted AR model
for(int n=Ncoef;n＜Npast+Nfut;n++)
{
double sum=0.0;
for(int i=1;i＜=Ncoef;i++)
{
if(n-i＜Npast) sum-=a[i]*x[n-i];
else sum-=a[i]*ym[Nfut+Npast-(n-i)];
}
if(n＜Npast) xm[Npast-1-n]=sum;
else ym[Nfut+Npast-n]=sum;
}
// Convert predictions from differences to prices
if(UseDiff)
{
double tmp=xm[0];
xm[0]=rates[0].open;
for(int i=1;i＜Npast-Ncoef;i++)
{
double tmp2=xm[i];
xm[i]=xm[i-1]-tmp;
tmp=tmp2;
}
}
ym[Nfut]=xm[0];
if(UseDiff)
{
for(int i=1;i＜=Nfut;i++)
ym[Nfut-i]+=ym[Nfut-i+1];
}
return(rates_total);
}
//==================================== FUNCTIONS =========================================
// Burg method --------------------------------------------------------------------------+
void Burg(double& x[],int n,int p,double& a[])
{
double df[],db[];
ArrayResize(df,n);
ArrayResize(db,n);
double tmp,num,den,r;
for(int i=0;i＜n;i++)
{
df[i]=x[i];
db[i]=x[i];
}
// Main loop
for(int k=1;k＜=p;k++)
{
// Calculate reflection coefficient
num=0.0;
den=0.0;
if(k==1)
{
for(int i=2;i＜n;i++)
{
num+=x[i-1]*(x[i]+x[i-2]);
den+=x[i-1]*x[i-1];
}
r=-num/den/2.0;
if(r> 1.0) r= 1.0;
if(r＜-1.0) r=-1.0;
}
else
{
for(int i=k;i＜n;i++)
{
num+=df[i]*db[i-1];
den+=(df[i]*df[i]+db[i-1]*db[i-1]);
}
r=-2.0*num/den;
}
// Calculate prediction coefficients
a[k]=r;
int kh=k/2;
for(int i=1;i＜=kh;i++)
{
int ki=k-i;
tmp=a[i];
a[i]+=r*a[ki];
if(i!=ki) a[ki]+=r*tmp;
}
if(k＜p)
// Calculate new residues
for(int i=n-1;i>=k;i--)
{
tmp=df[i];
df[i]+=r*db[i-1];
db[i]=db[i-1]+r*tmp;
}
}
}
【表示結果】
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