Article-23677-EGARCH-MQL5-Volatility-Modeling/TestsForAsymmetry.mq5

//+------------------------------------------------------------------+
//|                                            TestsForAsymmetry.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"
#define __SLSQP__
#property script_show_inputs
#include "Arch\Univariate\tests.mqh"
#include "Arch\Univariate\mean.mqh"
//--- input parameters
input ENUM_TIMEFRAMES  TimeFrame = PERIOD_D1;         //--- Data horizon interval
input datetime         StartDate = D'2026.01.01';     //--- Historical capture anchor start date
input ulong            HistoryLen = 2000;             //--- Total historical data bars to request
input ENUM_STAT_CONFIDENCE Statistical_Confidence=CONFIDENCE_95;//---Confidence level for p-value 
//+------------------------------------------------------------------+
//| Script program start function                                    |
//+------------------------------------------------------------------+
void OnStart()
  {
//---
   vector prices;
//--- --- Step 1: Historical Data Fetch ---
//--- Pull raw close prices into a high-performance vector array
   if(!prices.CopyRates(NULL, TimeFrame, COPY_RATES_CLOSE, StartDate, HistoryLen) || HistoryLen > prices.Size())
     {
      Print(" failed to get close prices for ", _Symbol, ". Error ", GetLastError());
      return;
     }

//--- --- Step 2: Transform Prices to Returns ---
//--- Map closing prices to logarithmic space
   prices = log(prices);

//--- Compute log returns: r_t = ln(P_t) - ln(P_{t-1})
   vector returns = np::diff(prices);
//---
   Print(_Symbol, " : ",EnumToString(TimeFrame)," : ", TimeToString(StartDate), " : ", string(prices.Size()));
   LeverageCorrelationResult lcr = LeverageCorrelationTest(returns,1,Statistical_Confidence);
   Print("**** Leverage Correlation Test ****");
   PrintFormat("Corr(r_t-1, r_t^2): %.4f \n p-value: %.4f",lcr.correlation,lcr.p_value);
   Print("Leverage correlation test's assertion of asymmetric volatility is ", lcr.significant_leverage_effect);
//---
   Print("**** Volatility Runs Test ****");
   VolatilityRunsResult vrr = VolatilityRunsAsymmetryTest(returns,Statistical_Confidence);
   PrintFormat("Probability of high volatility following a negative return %.8f",vrr.p_high_vol_prev_down);
   PrintFormat("Probability of high volatility following a positive return %.8f",vrr.p_high_vol_prev_up);
   PrintFormat("T_stat %.8f", vrr.chi2_stat);
   PrintFormat("Pvalue %.8f",vrr.p_value);
   Print("Volatility Runs test's assertion of asymmetric volatility is ", vrr.significant_asymmetry);
//---
   ArchParameters arch_params;
   arch_params.mean_model_type = MEAN_CONSTANT;
   arch_params.vol_model_type = VOL_GARCH;
   arch_params.observations = returns*100.;
//---
   ConstantMean ar_model;
//---
   if(!ar_model.initialize(arch_params))
     {
      Print("Failed to initialize the model");
      return;
     }
//---
   ArchModelResult model_result = ar_model.fit();
//---
   if(!model_result.params.Size())
      return;
//---
   returns = model_result.std_resid();
//---
   EngleNgResult enr = EngleNgSignBiasTest(returns,Statistical_Confidence);
   Print("**** Engle's NG sign bias test results ****");
   string effects[4] = {"const", "sign-bias", "neg_size_bias", "pos_size_bias"};
   PrintFormat("%-15s %-15s %-15s %-15s","Effect","Coeffs", "T_Stats","Pvalues");
//---
   for(uint i = 0; i<enr.coefficients.Size(); ++i)
      PrintFormat("%-15s %-15.8f %-15.8f %-15.8f", effects[i],enr.coefficients[i],enr.t_stats[i],enr.p_values[i]);
//---
   PrintFormat("a2_minus_a3 %.8f \na2_vs_a3 t_stat %.8f \na2_vs_a3 pvalue %.8f", enr.a2_minus_a3,enr.a2_vs_a3_t_stat,enr.a2_vs_a3_p_value);
   Print("Engle NG sign bias test's assertion of asymmetric volatility is ", enr.significant_asymmetry);
   
  }
//+------------------------------------------------------------------+