//+------------------------------------------------------------------+
//|                                              HAR_as_ARX_Demo.mq5 |
//|                                  Copyright 2025, MetaQuotes Ltd. |
//|                                             https://www.mql5.com |
//+------------------------------------------------------------------+
#property copyright "Copyright 2025, MetaQuotes Ltd."
#property link      "https://www.mql5.com"
#property version   "1.00"
#property script_show_inputs
#include<Arch\Univariate\mean.mqh>
//--- input parameters
input string   Symbol_="AUDUSD";
input ENUM_TIMEFRAMES   TimeFrame=PERIOD_D1;
input datetime StartDate=D'2025.01.01';
input ulong HistoryLen = 504;
input double ScaleFactor=100.;
input bool MeanConstant = true;
input string MeanLags ="1,5,22";
//+------------------------------------------------------------------+
//| Script program start function                                    |
//+------------------------------------------------------------------+
void OnStart()
  {
//---download data
   vector prices;
   if(!prices.CopyRates(Symbol_,TimeFrame,COPY_RATES_CLOSE,StartDate,HistoryLen))
    {
     Print(" failed to get close prices for ", Symbol_,". Error ", GetLastError());
     return;
    }
//---
   prices = log(prices);
//---
   vector returns = np::diff(prices);
//---
   string lag_info[];
//---
   vector lags=vector::Zeros(0);
//---
   int nlags = StringSplit(MeanLags,StringGetCharacter(",",0),lag_info);
//---
   double atod;
   if(nlags>0)
    {
     for(uint i = 0; i<uint(nlags); ++i)
      {
       if(StringLen(lag_info[i])>0)
        {
         atod = StringToDouble(lag_info[i]);
         if(atod>0 && ulong(atod)<returns.Size()-1)
           if(lags.Resize(lags.Size()+1,3))
              lags[lags.Size()-1] = atod;
        }
      }
    }
//---
  if(lags.Size())
    np::sort(lags);
//---build the HAR model
  ArchParameters har_spec;
  har_spec.observations=returns*ScaleFactor;
  har_spec.include_constant = MeanConstant;
  har_spec.mean_lags = lags;
  har_spec.vol_model_type = VOL_CONST;
//---
  HAR harmodel;
//---
  if(!harmodel.initialize(har_spec))
    return;
//---
  ArchModelResult har = harmodel.fit(ScaleFactor);
//---
  if(!har.params.Size())
   {
    Print("Convergence failed ", GetLastError());
    return;
   }
//---
  Print(" Har model parameters\n", har.params);
//---Now we build an equivalent ARX model
  matrix exogvars = matrix::Zeros(returns.Size(),lags.Size());
//---calculate averages  
  double sum;
  ulong lag,count;
  for(ulong i = 0; i<exogvars.Cols(); ++i)
   {
    lag = (ulong)lags[i];
    count = lag;
    for(ulong k = lag; k<exogvars.Rows(); ++k)
     {
       sum = 0.0;
       for(ulong j = 0; j<count; ++j)
         sum+=returns[k-j-1];
       exogvars[k,i] = sum/double(count);
     }
   }
//---
  ArchParameters arx_spec;
  arx_spec.observations = ScaleFactor*np::sliceVector(returns,long(lags[lags.Size()-1]));
  arx_spec.exog_data = ScaleFactor*np::sliceMatrixRows(exogvars,long(lags[lags.Size()-1]));
  arx_spec.include_constant = MeanConstant;
  arx_spec.vol_model_type=VOL_CONST; 
//---
  ARX arxmodel;
  if(!arxmodel.initialize(arx_spec))
   return;
//---
  ArchModelResult arx = arxmodel.fit(ScaleFactor);
  if(!arx.params.Size())
   {
    Print(" convergence failed ", GetLastError());
    return;
   }
//---
  Print("ARX model parameters\n", arx.params);
 } 
//+------------------------------------------------------------------+