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main_others_CC_MGARCH.cpp
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#include <iostream>
#include <fstream>
#include <iomanip> // format manipulation
#include <string>
#include <sstream>
#include <cstdlib>
#include <math.h>
#include <cmath>
#include <numeric>
#include <stdio.h>
#include <map>
#include <unistd.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_multimin.h>
#include <gsl/gsl_bspline.h>
#include <vector> // C++ vector class
#include <algorithm>
#include <functional>
#include <gsl/gsl_randist.h>
#include <boost/numeric/conversion/cast.hpp>
#include <boost/lexical_cast.hpp>
#include <gsl/gsl_rng.h>
#include <unistd.h>
#include <filein.h>
#include <limits>
#include <float.h>
#include <time.h>
#include <sys/time.h>
#include <chrono>
//#include <windows.h>
#include <omp.h>
#include <sys/stat.h>
#include <sys/types.h>
#include <matrix_ops2.h>
#include <dist_corr.h>
#include <kernel.h>
//#include <power.h>
#include <tests.h>
#include <nl_dgp.h>
//#include <nongaussian_reg.h>
#include <dep_tests.h>
//#include <nongaussian_dist_corr.h>
//#include <VAR_gLasso.h>
//#include <student_reg.h>
#include <plot.h>
#include "utils.h"
#include <shogun/mathematics/Math.h>
#include <shogun/mathematics/Statistics.h>
#include <shogun/lib/SGSparseVector.h>
#include <shogun/lib/config.h>
//#include <shogun/base/init.h>
//#include <shogun/base/some.h>
#include <shogun/ensemble/MajorityVote.h>
#include <shogun/evaluation/MeanSquaredError.h>
#include <shogun/labels/RegressionLabels.h>
#include <shogun/lib/SGMatrix.h>
#include <shogun/lib/SGVector.h>
#include <shogun/loss/SquaredLoss.h>
#include <shogun/machine/RandomForest.h>
#include <shogun/machine/StochasticGBMachine.h>
#include <shogun/multiclass/tree/CARTree.h>
#include <shogun/util/iterators.h>
#include <shogun/mathematics/linalg/LinalgNamespace.h>
#include <shogun/mathematics/linalg/linop/MatrixOperator.h>
#include <shogun/labels/BinaryLabels.h>
#include <shogun/features/DenseFeatures.h>
#include <shogun/kernel/GaussianKernel.h>
#include <shogun/classifier/svm/LibSVM.h>
#include <shogun/lib/common.h>
#include <shogun/io/SGIO.h>
#include <shogun/io/File.h>
//#include <ShogunML/ml_reg_6_1_4.h>
#include <ShogunML/data/data.h>
//#include <ShogunML/tscv.h>
//#include <ML_reg_dcorr.h>
#include <ML_dcorr.h>
#include <mgarch.h>
#include <nmsimplex.h>
#include <hsic_test.h>
#include <ML_dcorr_power.h>
#include <others_power.h>
#define CHUNK 1
using namespace std;
using namespace shogun;
using namespace shogun::linalg;//void (*aktfgv)(double *,double *,int *,int *,void *,Matrix&);
int main(void) {
//start the timer%%%%%
//time = ((double) clock())/((double) CLOCKS_PER_SEC);
auto time = std::chrono::high_resolution_clock::now();
auto timelast = time;
//# if 0 //begin comment
/************************************************************************************************************************************************************/
/************ Start the Simulations for Wang et al.'s (2021) HSIC-based test, El Himdi and Roy's (1997), Bouhaddioui and Roy's (2006),
Robbins and Fisher's (2015), and Tchahou and Duchesne's (2013) tests ********************************************/
/***************************************************** True DGP: CC-MGARCH and Fitted GDP: CC-MGARCH *******************************************************/
int number_sampl = 500; /*number of random samples to be drawn*/
int num_bts = 500; /*number of bootstrap samples as in Wang et al. (2021)*/
int T = 100;
int lag_smooth = 7; /*3, 5, 7, 10, 20, 25*/
double h = 0.; /*a differential factor to compute numerical derivatives*/
unsigned long int seed = 12425;
/* define VAR(1) parameters */
SGVector<double> theta_var1(4), theta_var2(4);
theta_var1[0] = 0.4;
theta_var1[1] = 0.1;
theta_var1[2] = -1.;
theta_var1[3] = 0.5;
theta_var2[0] = -1.5;
theta_var2[1] = 1.2;
theta_var2[2] = -0.9;
theta_var2[3] = 0.5;
/* define CC-MGARCH parameters */
int dim = 7;
SGVector<double> theta_mgarch1(dim), theta_mgarch2(dim);
double theta_mgarch1a[dim] = {0.2, 0.8, 0.1, 0.2, 0.8, 0.1, 0.5};
for (int i = 0; i < dim; ++i)
theta_mgarch1[i] = theta_mgarch1a[i];
theta_mgarch1.display_vector("theta_mgarch1");
double theta_mgarch2a[dim] = {0.2, 0.8, 0.1, 0.2, 0.8, 0.1, 0.5};
for (int i = 0; i < dim; ++i)
theta_mgarch2[i] = theta_mgarch2a[i];
theta_mgarch2.display_vector("theta_mgarch2");
Matrix HSIC_J1_REJF(2,1), HSIC_J2_REJF(2,1), ER_asymp_REJF(2,1), ER_empir_CV(2,1), BR_asymp_REJF(2,1), BR_empir_CV(2,1), RbF_asymp_REJF(2,1), \
RbF_empir_CV(2,1), TD_L1_asymp_REJF(2,1), TD_L1_empir_CV(2,1), TD_T1_asymp_REJF(2,1), TD_T1_empir_CV(2,1);
Matrix HSIC_J1_empir_REJF(2,1), HSIC_J2_empir_REJF(2,1), ER_empir_REJF(2,1), BR_empir_REJF(2,1), RbF_empir_REJF(2,1), TD_L1_empir_REJF(2,1), \
TD_T1_empir_REJF(2,1);
Matrix ER_asymp_CV(2,1), BR_asymp_CV(2,1), RbF_asymp_CV(2,1), TD_L1_asymp_CV(2,1), TD_T1_asymp_CV(2,1);
BR_asymp_CV(1) = 1.645; //5%-critical value from the standard normal distribution
BR_asymp_CV(2) = 1.28; //10%-critical value from the standard normal distribution
ER_asymp_CV = Dep_tests::asymp_CV_ChiSq3(lag_smooth);
RbF_asymp_CV = Dep_tests::asymp_CV_Gamma(lag_smooth, 2, 2);
TD_L1_asymp_CV = Dep_tests::asymp_CV_ChiSq(lag_smooth);
TD_T1_asymp_CV = Dep_tests::asymp_CV_ChiSq4(lag_smooth);
const char *new_dir;
string dir_name, output_filename, size_filename, power_filename;
ofstream output, size_out, pwr_out;
bool use_bartlett_ker = false;
int choose_alt = 0;
//*************************************************************using the Bartlett kernel****************************************************************************/
// Creating a directory
dir_name = "./Results/Others/CC-MGARCH/BL/";
new_dir = dir_name.c_str();
if (mkdir(new_dir, 0777) == -1)
cerr << "Error : " << strerror(errno) << endl;
else
cout << "Directory created" << endl;
output_filename = dir_name + "file_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_bartlett_kernel_cc_mgarch.txt";
size_filename = dir_name + "size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_bartlett_kernel_cc_mgarch.txt";
power_filename = dir_name + "power_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_bartlett_kernel_cc_mgarch.txt";
output.open (output_filename.c_str(), ios::out);
size_out.open (size_filename.c_str(), ios::out);
pwr_out.open (power_filename.c_str(), ios::out);
output << std::fixed << std::setprecision(5);
output << "T = " << T << " and Lag smooth length = " << lag_smooth << endl;
//calculate empirical critical values and sizes
Others_power::cValue<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,bartlett_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_asymp_REJF, /*asymptotic rejection rates of El Himdi and Roy's (1997) test*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
BR_asymp_REJF, /*asymptotic rejection rates of Bouhaddioui and Roy's (2006) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
RbF_asymp_REJF, /*asymptotic rejection rates of Robbins and Fisher's (2015) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
TD_L1_asymp_REJF, /*asymptotic rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_asymp_REJF, /*asymptotic rejection rates of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of and Robbins and Fisher's (2015) test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
h,
seed,
size_out);
output << "The HSIC-based J1 test: Empirical 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << HSIC_J1_REJF(1) \
<< " , " << HSIC_J1_REJF(2) << ")" << endl;
output << "The HSIC-based J2 test: Empirical 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << HSIC_J2_REJF(1) \
<< " , " << HSIC_J2_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << ER_asymp_CV(1) \
<< " , " << ER_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << ER_empir_CV(1) \
<< " , " << ER_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << ER_asymp_REJF(1) \
<< " , " << ER_asymp_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << BR_asymp_CV(1) \
<< " , " << BR_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << BR_empir_CV(1) \
<< " , " << BR_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << BR_asymp_REJF(1) \
<< " , " << BR_asymp_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << RbF_asymp_CV(1) \
<< " , " << RbF_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << RbF_empir_CV(1) \
<< " , " << RbF_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << RbF_asymp_REJF(1) \
<< " , " << RbF_asymp_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << TD_L1_asymp_CV(1) \
<< " , " << TD_L1_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << TD_L1_empir_CV(1) \
<< " , " << TD_L1_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << TD_L1_asymp_REJF(1) \
<< " , " << TD_L1_asymp_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << TD_T1_asymp_CV(1) \
<< " , " << TD_T1_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << TD_T1_empir_CV(1) \
<< " , " << TD_T1_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << TD_T1_asymp_REJF(1) \
<< " , " << TD_T1_asymp_REJF(2) << ")" << endl;
//calculate rejection rates
choose_alt = 1; //correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,bartlett_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of Robbins and Fisher's (2015) test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
choose_alt, /*set a degree of dependence between two DGPs*/
h, /*a finite differential factor*/
seed, /*seed for random number generator*/
pwr_out);
output << "========================================================================================================================================" << endl;
output << "choose_alt = " << choose_alt << endl;
output << "Wang et al.'s (2021) HSIC-based J1 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J1_REJF(1) << " , " << HSIC_J1_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Wang et al.'s (2021) HSIC-based J2 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J2_REJF(1) << " , " << HSIC_J2_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_asymp_REJF(1) << " , " << ER_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_empir_REJF(1) << " , " << ER_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_asymp_REJF(1) << " , " << BR_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_empir_REJF(1) << " , " << BR_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_asymp_REJF(1) << " , " << RbF_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_empir_REJF(1) << " , " << RbF_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_asymp_REJF(1) << " , " << TD_L1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_empir_REJF(1) << " , " << TD_L1_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_asymp_REJF(1) << " , " << TD_T1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_empir_REJF(1) << " , " << TD_T1_empir_REJF(2) \
<< ")" << endl;
output << "=======================================================================================================================================" << endl;
choose_alt = 2; //non-correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,bartlett_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of Robbins and Fisher's (2015) test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
choose_alt, /*set a degree of dependence between two DGPs*/
h, /*a finite differential factor*/
seed, /*seed for random number generator*/
pwr_out);
output << "========================================================================================================================================" << endl;
output << "choose_alt = " << choose_alt << endl;
output << "Wang et al.'s (2021) HSIC-based J1 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J1_REJF(1) << " , " << HSIC_J1_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Wang et al.'s (2021) HSIC-based J2 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J2_REJF(1) << " , " << HSIC_J2_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_asymp_REJF(1) << " , " << ER_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_empir_REJF(1) << " , " << ER_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_asymp_REJF(1) << " , " << BR_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_empir_REJF(1) << " , " << BR_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_asymp_REJF(1) << " , " << RbF_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_empir_REJF(1) << " , " << RbF_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_asymp_REJF(1) << " , " << TD_L1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_empir_REJF(1) << " , " << TD_L1_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_asymp_REJF(1) << " , " << TD_T1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_empir_REJF(1) << " , " << TD_T1_empir_REJF(2) \
<< ")" << endl;
output << "=======================================================================================================================================" << endl;
choose_alt = 3; //non-correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,bartlett_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of Robbins and Fisher's (2015) test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
choose_alt, /*set a degree of dependence between two DGPs*/
h, /*a finite differential factor*/
seed, /*seed for random number generator*/
pwr_out);
output << "========================================================================================================================================" << endl;
output << "choose_alt = " << choose_alt << endl;
output << "Wang et al.'s (2021) HSIC-based J1 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J1_REJF(1) << " , " << HSIC_J1_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Wang et al.'s (2021) HSIC-based J2 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J2_REJF(1) << " , " << HSIC_J2_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_asymp_REJF(1) << " , " << ER_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_empir_REJF(1) << " , " << ER_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_asymp_REJF(1) << " , " << BR_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_empir_REJF(1) << " , " << BR_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_asymp_REJF(1) << " , " << RbF_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_empir_REJF(1) << " , " << RbF_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_asymp_REJF(1) << " , " << TD_L1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_empir_REJF(1) << " , " << TD_L1_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_asymp_REJF(1) << " , " << TD_T1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_empir_REJF(1) << " , " << TD_T1_empir_REJF(2) \
<< ")" << endl;
output << "=======================================================================================================================================" << endl;
choose_alt = 4; //non-correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,bartlett_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of Robbins and Fisher's (2015) test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
choose_alt, /*set a degree of dependence between two DGPs*/
h, /*a finite differential factor*/
seed, /*seed for random number generator*/
pwr_out);
output << "========================================================================================================================================" << endl;
output << "choose_alt = " << choose_alt << endl;
output << "Wang et al.'s (2021) HSIC-based J1 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J1_REJF(1) << " , " << HSIC_J1_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Wang et al.'s (2021) HSIC-based J2 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J2_REJF(1) << " , " << HSIC_J2_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_asymp_REJF(1) << " , " << ER_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_empir_REJF(1) << " , " << ER_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_asymp_REJF(1) << " , " << BR_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_empir_REJF(1) << " , " << BR_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_asymp_REJF(1) << " , " << RbF_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_empir_REJF(1) << " , " << RbF_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_asymp_REJF(1) << " , " << TD_L1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_empir_REJF(1) << " , " << TD_L1_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_asymp_REJF(1) << " , " << TD_T1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_empir_REJF(1) << " , " << TD_T1_empir_REJF(2) \
<< ")" << endl;
output << "=======================================================================================================================================" << endl;
choose_alt = 5; //strongly correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,bartlett_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of Robbins and Fisher's (2015) test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
choose_alt, /*set a degree of dependence between two DGPs*/
h, /*a finite differential factor*/
seed, /*seed for random number generator*/
pwr_out);
output << "========================================================================================================================================" << endl;
output << "choose_alt = " << choose_alt << endl;
output << "Wang et al.'s (2021) HSIC-based J1 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J1_REJF(1) << " , " << HSIC_J1_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Wang et al.'s (2021) HSIC-based J2 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J2_REJF(1) << " , " << HSIC_J2_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_asymp_REJF(1) << " , " << ER_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_empir_REJF(1) << " , " << ER_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_asymp_REJF(1) << " , " << BR_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_empir_REJF(1) << " , " << BR_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_asymp_REJF(1) << " , " << RbF_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_empir_REJF(1) << " , " << RbF_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_asymp_REJF(1) << " , " << TD_L1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_empir_REJF(1) << " , " << TD_L1_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_asymp_REJF(1) << " , " << TD_T1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_empir_REJF(1) << " , " << TD_T1_empir_REJF(2) \
<< ")" << endl;
output << "=======================================================================================================================================" << endl;
output.close(); //close file streams
size_out.close();
pwr_out.close();
//***********************************************************using the Daniell kernel*************************************************************************
// Creating a directory
dir_name = "/Results/Others/CC-MGARCH/DN/";
new_dir = dir_name.c_str();
if (mkdir(new_dir, 0777) == -1)
cerr << "Error : " << strerror(errno) << endl;
else
cout << "Directory created" << endl;
output_filename = dir_name + "file_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_daniell_kernel_cc_mgarch.txt";
size_filename = dir_name + "size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_daniell_kernel_cc_mgarch.txt";
power_filename = dir_name + "power_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_daniell_kernel_cc_mgarch.txt";
output.open (output_filename.c_str(), ios::out);
size_out.open (size_filename.c_str(), ios::out);
pwr_out.open (power_filename.c_str(), ios::out);
output << std::fixed << std::setprecision(5);
output << "T = " << T << " and Lag smooth length = " << lag_smooth << endl;
//calculate empirical critical values and sizes
Others_power::cValue<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,daniell_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_asymp_REJF, /*asymptotic rejection rates of El Himdi and Roy's (1997) test*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
BR_asymp_REJF, /*asymptotic rejection rates of Bouhaddioui and Roy's (2006) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
RbF_asymp_REJF, /*asymptotic rejection rates of Robbins and Fisher's (2015) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
TD_L1_asymp_REJF, /*asymptotic rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_asymp_REJF, /*asymptotic rejection rates of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of and Robbins and Fisher's (2015) test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
h,
seed,
size_out,
use_bartlett_ker);
output << "The HSIC-based J1 test: Empirical 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << HSIC_J1_REJF(1) \
<< " , " << HSIC_J1_REJF(2) << ")" << endl;
output << "The HSIC-based J2 test: Empirical 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << HSIC_J2_REJF(1) \
<< " , " << HSIC_J2_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << ER_asymp_CV(1) \
<< " , " << ER_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << ER_empir_CV(1) \
<< " , " << ER_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << ER_asymp_REJF(1) \
<< " , " << ER_asymp_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << BR_asymp_CV(1) \
<< " , " << BR_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << BR_empir_CV(1) \
<< " , " << BR_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << BR_asymp_REJF(1) \
<< " , " << BR_asymp_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << RbF_asymp_CV(1) \
<< " , " << RbF_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << RbF_empir_CV(1) \
<< " , " << RbF_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << RbF_asymp_REJF(1) \
<< " , " << RbF_asymp_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << TD_L1_asymp_CV(1) \
<< " , " << TD_L1_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << TD_L1_empir_CV(1) \
<< " , " << TD_L1_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << TD_L1_asymp_REJF(1) \
<< " , " << TD_L1_asymp_REJF(2) << ")" << endl;
output << "==================================================================================================================" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << TD_T1_asymp_CV(1) \
<< " , " << TD_T1_asymp_CV(2) << ")" << endl;
output << "Empirical 5%- and 10%- critical values for lag_smooth = " << lag_smooth << " are " << "(" << TD_T1_empir_CV(1) \
<< " , " << TD_T1_empir_CV(2) << ")" << endl;
output << "Asymptotic 5%- and 10%- sizes for lag_smooth = " << lag_smooth << " are " << "(" << TD_T1_asymp_REJF(1) \
<< " , " << TD_T1_asymp_REJF(2) << ")" << endl;
//calculate rejection rates
choose_alt = 1; //correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,daniell_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of Robbins and Fisher's (2015) test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
choose_alt, /*set a degree of dependence between two DGPs*/
h, /*a finite differential factor*/
seed, /*seed for random number generator*/
pwr_out,
use_bartlett_ker);
output << "========================================================================================================================================" << endl;
output << "choose_alt = " << choose_alt << endl;
output << "Wang et al.'s (2021) HSIC-based J1 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J1_REJF(1) << " , " << HSIC_J1_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Wang et al.'s (2021) HSIC-based J2 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J2_REJF(1) << " , " << HSIC_J2_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_asymp_REJF(1) << " , " << ER_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_empir_REJF(1) << " , " << ER_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_asymp_REJF(1) << " , " << BR_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_empir_REJF(1) << " , " << BR_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_asymp_REJF(1) << " , " << RbF_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_empir_REJF(1) << " , " << RbF_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_asymp_REJF(1) << " , " << TD_L1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_empir_REJF(1) << " , " << TD_L1_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_asymp_REJF(1) << " , " << TD_T1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_empir_REJF(1) << " , " << TD_T1_empir_REJF(2) \
<< ")" << endl;
output << "=======================================================================================================================================" << endl;
choose_alt = 2; //non-correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,daniell_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of Robbins and Fisher's (2015) test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
choose_alt, /*set a degree of dependence between two DGPs*/
h, /*a finite differential factor*/
seed, /*seed for random number generator*/
pwr_out,
use_bartlett_ker);
output << "========================================================================================================================================" << endl;
output << "choose_alt = " << choose_alt << endl;
output << "Wang et al.'s (2021) HSIC-based J1 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J1_REJF(1) << " , " << HSIC_J1_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Wang et al.'s (2021) HSIC-based J2 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J2_REJF(1) << " , " << HSIC_J2_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_asymp_REJF(1) << " , " << ER_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_empir_REJF(1) << " , " << ER_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_asymp_REJF(1) << " , " << BR_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_empir_REJF(1) << " , " << BR_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_asymp_REJF(1) << " , " << RbF_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_empir_REJF(1) << " , " << RbF_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_asymp_REJF(1) << " , " << TD_L1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_empir_REJF(1) << " , " << TD_L1_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_asymp_REJF(1) << " , " << TD_T1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_empir_REJF(1) << " , " << TD_T1_empir_REJF(2) \
<< ")" << endl;
output << "=======================================================================================================================================" << endl;
choose_alt = 3; //non-correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,daniell_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
num_bts, /*number of bootstrap samples*/
ER_empir_CV, /*5% and 10% empirical critical values of El Himdi and Roy's (1997) test*/
ER_asymp_CV, /*5% and 10% asymptotic critical values of El Himdi and Roy's (1997) test*/
BR_empir_CV, /*5% and 10% empirical critical values of Bouhaddioui and Roy's (2006) test*/
BR_asymp_CV, /*5% and 10% asymptotic critical values of Bouhaddioui and Roy's (2006) test*/
RbF_empir_CV, /*5% and 10% empirical critical values of Robbins and Fisher's (2015) test*/
RbF_asymp_CV, /*5% and 10% asymptotic critical values of Robbins and Fisher's (2015) test*/
TD_L1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_L1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_CV, /*5% and 10% empirical critical values of Tchahou and Duchesne's (2013) T1 test*/
TD_T1_asymp_CV, /*5% and 10% asymptotic critical values of Tchahou and Duchesne's (2013) T1 test*/
choose_alt, /*set a degree of dependence between two DGPs*/
h, /*a finite differential factor*/
seed, /*seed for random number generator*/
pwr_out,
use_bartlett_ker);
output << "========================================================================================================================================" << endl;
output << "choose_alt = " << choose_alt << endl;
output << "Wang et al.'s (2021) HSIC-based J1 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J1_REJF(1) << " , " << HSIC_J1_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Wang et al.'s (2021) HSIC-based J2 test:" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << HSIC_J2_REJF(1) << " , " << HSIC_J2_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "El Himdi and Roy's (1997) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_asymp_REJF(1) << " , " << ER_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << ER_empir_REJF(1) << " , " << ER_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Bouhaddioui and Roy's (2006) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_asymp_REJF(1) << " , " << BR_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << BR_empir_REJF(1) << " , " << BR_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Robbins and Fisher's (2015) test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_asymp_REJF(1) << " , " << RbF_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << RbF_empir_REJF(1) << " , " << RbF_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) L1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_asymp_REJF(1) << " , " << TD_L1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_L1_empir_REJF(1) << " , " << TD_L1_empir_REJF(2) \
<< ")" << endl;
output << "----------------------------------------------------------------------------------------------------------------------------------------" << endl;
output << "Tchahou and Duchesne's (2013) T1 test:" << endl;
output << "Asymptotic 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_asymp_REJF(1) << " , " << TD_T1_asymp_REJF(2) \
<< ")" << endl;
output << "Empirical 5%- and 10%- rejection rates for choose_alt = " << choose_alt << ": " << "(" << TD_T1_empir_REJF(1) << " , " << TD_T1_empir_REJF(2) \
<< ")" << endl;
output << "=======================================================================================================================================" << endl;
choose_alt = 4; //non-correlated errors
Others_power::power_f<NL_Dgp::gen_CC_MGARCH,HSIC::kernel,HSIC::kernel,cc_mgarch::mle_simplex,NL_Dgp::gen_CC_MGARCH,NL_Dgp::resid_CC_MGARCH,\
cc_mgarch::neg_loglikelihood_gradient, cc_mgarch::neg_loglikelihood_hessian,daniell_kernel> \
( HSIC_J1_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J1 test*/
HSIC_J2_REJF, /*rejection rates of Wang et al.'s (2021) HSIC-based J2 test*/
ER_empir_REJF, ER_asymp_REJF, /*rejection rates of El Himdi and Roy's (1997) test*/
BR_empir_REJF, BR_asymp_REJF, /*rejection rates of Bouhaddioui and Roy's (2006) test*/
RbF_empir_REJF, RbF_asymp_REJF, /*rejection rates of and Robbins and Fisher's (2015) test*/
TD_L1_empir_REJF, TD_L1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) L1 test*/
TD_T1_empir_REJF, TD_T1_asymp_REJF, /*rejection rates of Tchahou and Duchesne's (2013) T1 test*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*initial values used to estimate DGPs*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/