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main_VAR_CC_MGARCH_MGARCH_data.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 <nl_dgp.h>
#include <dep_tests.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 <VAR_CC_MGARCH_dcorr_power.h>
#define CHUNK 1
using namespace std;
using namespace shogun;
using namespace shogun::linalg;
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 the Proposed Test ********************************************************************/
/************************************************** True DGP: CC_MGARCH(1) and Fitted DGP: VAR-CC-MGARCH(1,1) ***************************************************************/
unsigned long int seed = 1535;
int T = 200;
int lag_smooth = 5; // set M_T = 3, 5, 7, 10, 20, and 25
double expn = 1.5;
int number_sampl = 500;
int num_B = 500;
/* define CC-MGARCH parameters */
SGVector<double> theta_mgarch1 {0.2, 0.8, 0.1, 0.2, 0.8, 0.1, 0.5};
theta_mgarch1.display_vector("theta_mgarch1");
SGVector<double> theta_mgarch2 {0.2, 0.8, 0.1, 0.2, 0.8, 0.1, 0.5};
theta_mgarch2.display_vector("theta_mgarch2");
// /* define VAR-CC-MGARCH parameters */
// SGVector<double> theta_var_mgarch1 {0.4, 0.1, -1., 0.5, 0.2, 0.8, 0.1, 0.2, 0.8, 0.1, 0.5};
// SGVector<double> theta_var_mgarch2 {-1.5, 1.2, -0.9, 0.5, 0.2, 0.8, 0.1, 0.2, 0.8, 0.1, 0.5};
//![Generate two independent sequences of i.i.d. standard normal random variables]
gsl_rng *r;
const gsl_rng_type *gen;//random number generator
gsl_rng_env_setup();
gen = gsl_rng_default;
r = gsl_rng_alloc(gen);
gsl_rng_set(r, seed);
SGMatrix<double> xi_x(num_B, T), xi_y(num_B, T);
for (auto i = 0; i < num_B; i++) {
for (auto t = 0; t < T; t++) {
xi_x(i,t) = gsl_ran_ugaussian (r);
xi_y(i,t) = gsl_ran_ugaussian (r);
}
}
gsl_rng_free(r); // free up memory
const char *new_dir;
string dir_name, output_filename, size_filename, power_filename;
ofstream output, size_out, pwr_out;
Matrix asymp_CV(2,1), empir_REJF(2,1), empir_CV(2,1), asymp_REJF(2,1), bootstrap_REJF(2, 1);
asymp_CV(1) = 1.645; //5%-critical value from the standard normal distribution
asymp_CV(2) = 1.28; //10%-critical value from the standard normal distribution
output << std::fixed << std::setprecision(5);
/************************************************************ Using the Bartlett kernel ***********************************************************************/
// Creating a directory
dir_name = "./Results/VAR_CC_MGARCH/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) + "_expn=" + std::to_string(expn)
+ "_bartlett_kernel_mgarch_data.txt";
size_filename = dir_name + "size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_bartlett_kernel_mgarch_data.txt";
power_filename = dir_name + "power_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_bartlett_kernel_mgarch_data.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 << "Lag smooth length = " << lag_smooth << endl;
int choose_alt = 0;
size_out << "====================================================== Compute sizes ==================================================" << endl;
//calculate 5%- and 10%- asymptotic sizes and empirical critical values
VAR_CC_MGARCH_dcorr_power::cValue<NL_Dgp::gen_CC_MGARCH, bartlett_kernel> (asymp_REJF, empir_CV,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
seed,
size_out);
output << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
cout << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5% - and 10% - bootstrap sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5% - and 10% - bootstrap sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
size_out << "======================================================== Done with calculation of sizes ====================================================" << endl;
choose_alt = 1; //correlation (between eta1 and eta2) = 0.3
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, bartlett_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 2; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, bartlett_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 3; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, bartlett_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 4; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, bartlett_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 5; //the errors (eta1 and eta2) are highly correlated
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, bartlett_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
output.close();
size_out.close();
pwr_out.close();
/***************************************************************** Using the Daniell kernel ***********************************************************************/
// Creating a directory
dir_name = "./Results/VAR_CC_MGARCH/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) + "_expn=" + std::to_string(expn)
+ "_daniell_kernel_mgarch_data.txt";
size_filename = dir_name + "size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_daniell_kernel_mgarch_data.txt";
power_filename = dir_name + "power_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_daniell_kernel_mgarch_data.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 << "Lag smooth length = " << lag_smooth << endl;
choose_alt = 0;
size_out << "====================================================== Compute sizes ==================================================" << endl;
//calculate 5%- and 10%- asymptotic sizes and empirical critical values
VAR_CC_MGARCH_dcorr_power::cValue<NL_Dgp::gen_CC_MGARCH, daniell_kernel> (asymp_REJF, empir_CV,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
seed,
size_out);
output << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
cout << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5% - and 10% - bootstrap sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5% - and 10% - bootstrap sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
size_out << "======================================================== Done with calculation of sizes ====================================================" << endl;
choose_alt = 1; //correlation (between eta1 and eta2) = 0.3
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, daniell_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 2; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, daniell_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 3; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, daniell_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 4; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, daniell_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 5; //the errors (eta1 and eta2) are highly correlated
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, daniell_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
output.close();
size_out.close();
pwr_out.close();
/************************************************************ Using the QS kernel ***********************************************************************/
// Creating a directory
dir_name = "./Results/VAR_CC_MGARCH/CC_MGARCH/QS/";
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) + "_expn=" + std::to_string(expn)
+ "_QS_kernel_mgarch_data.txt";
size_filename = dir_name + "size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_QS_kernel_mgarch_data.txt";
power_filename = dir_name + "power_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_QS_kernel_mgarch_data.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 << "Lag smooth length = " << lag_smooth << endl;
choose_alt = 0;
size_out << "====================================================== Compute sizes ==================================================" << endl;
//calculate 5%- and 10%- asymptotic sizes and empirical critical values
VAR_CC_MGARCH_dcorr_power::cValue<NL_Dgp::gen_CC_MGARCH, QS_kernel> (asymp_REJF, empir_CV,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
seed,
size_out);
output << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
cout << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5% - and 10% - bootstrap sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5% - and 10% - bootstrap sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
size_out << "======================================================== Done with calculation of sizes ====================================================" << endl;
choose_alt = 1; //correlation (between eta1 and eta2) = 0.3
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, QS_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 2; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, QS_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 3; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, QS_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 4; //the errors (eta1 and eta2) are not correlated, but dependent
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, QS_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
choose_alt = 5; //the errors (eta1 and eta2) are highly correlated
pwr_out << "===================================================== Compute power =================================================" << endl;
VAR_CC_MGARCH_dcorr_power::power_f<NL_Dgp::gen_CC_MGARCH, QS_kernel>(empir_REJF, asymp_REJF,
bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta_mgarch1, theta_mgarch2, /*true parameters of two DGPs*/
theta_mgarch1, theta_mgarch2, /*7 by 1 vector of initial values
used to initialize the MLE estimator for VAR-CC-MGARCH(1,1)*/
number_sampl, /*number of random samples drawn*/
T, /*sample size*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
empir_CV, /*5% and 10% empirical critical values*/
asymp_CV, /*5% and 10% asymptotic critical values*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - bootstrap rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
pwr_out << "====================================================== Done with power calculation =============================================================" << endl;
output.close();
size_out.close();
pwr_out.close();
/***************************************** Finish the Simulations for the Proposed Test *********************************************************************/
/************************************************************************************************************************************************************/
//#endif //end comment
#if 0 //begin comment
/* Calculate empirical levels of a test */
//Import a column of data
ifstream data;
data.open("e:/Dropbox/Codes/Supermicro-Office-1/Exogeneity/Results/HimdiRoy/size_out_T=200_lag_smooth=25_threshold=1.54_bivariate.txt", ios::in);
if (!data)
return(EXIT_FAILURE);
vector<string> data1;
loadCSV(data, data1);
int N = data1.size(); //Rows
Matrix X(N, 1);
for (auto i = 1; i <= N; i++)
X(i) = hex2d(data1[i-1]);
data.close();
int count10 = 0, count5 = 0;
Dep_tests dep_obj;
Matrix cv(2, 1);
int bandW = 25; //set a lag-smoothing parameter
cv = dep_obj.asymp_CV_ChiSq2 (bandW);
for (auto i = 1; i <= N; ++i) {
if (X(i) >= cv(2)) ++count10;
if (X(i) >= cv(1)) ++count5;
}
cout << "N = " << N << endl;
cout << "10% rejection rate = " << ((double) count10/N) << endl;
cout << "5% rejection rate = " << ((double) count5/N) << endl;
/*//Import a csv file
ifstream data;
data.open("./Results/Others/Correlation/QS/size_out_T=200_lag_smooth=25_rho=0.80000000000000004.txt", ios::in);
if (!data)
return(EXIT_FAILURE);
vector<vector<string>* > data1;
loadCSV(data, data1);
int nR = data1.size(); //Rows
int nC = (*data1[1]).size(); //Columns
Matrix X(nR,nC);
for (auto i = 1; i <= nR; i++)
{
for (int j = 1; j <= nC; j++)
{
X(i,j) = hex2d((*data1[i-1])[j-1]);
}
}
for (vector<vector<string>*>::iterator p = data1.begin( ); p != data1.end( ); ++p)
{
delete *p;
}
data.close();
Matrix count10(nC, 1), count5(nC, 1), asymp_cv_Haugh(2, 1);
int bandW = 25; //set a lag-smoothing parameter
Dep_tests dep_obj;
asymp_cv_Haugh = dep_obj.asymp_CV_ChiSq (bandW);
for (auto i = 1; i <= nR; ++i) {
if (X(i,1) >= 1.28) ++count10(1);
if (X(i,1) >= 1.645) ++count5(1);
if (X(i,2) >= asymp_cv_Haugh(2)) ++count10(2);
if (X(i,2) >= asymp_cv_Haugh(1)) ++count5(2);
}
cout << "N = " << nR << endl;
for (auto j = 1; j <= nC; ++j) {
cout << "Test = " << j << ": 10% rejection rate = " << ((double) count10(j)/nR) << endl;
cout << "Test = " << j << ": 5% rejection rate = " << ((double) count5(j)/nR) << endl;
}*/
#endif //end comment
#if 0 //begin comment
/************************************** Start the Simulations for the Proposed Test: The Univariate Skewed-Normal Case **************************************/
/************************************************************************************************************************************************************/
int TL = 2;
int T = 100;
int N = 1000;
int number_sampl = 500;
double expn = 1.5, delta = 0.7, rho = 0.8;
int choose_alt = 0;
unsigned long seed = 856764325;
string output_filename, size_filename, power_filename;
ofstream output, size_out, pwr_out;
int lag_smooth = 5; //set M_T = 5, 10, 20, and 25
//============================================================= Bilinear Models ===============================================================================/
Matrix asymp_CV(2,1), empir_REJF(2,1), empir_CV(2,1), asymp_REJF(2,1), alpha_X(6,1), alpha_Y(6,1), epsilon_t(N,1), epsilon_s(N,1), eta_t(N,1), eta_s(N,1);
asymp_CV(1) = 1.645; //5%-critical value from the standard normal distribution
asymp_CV(2) = 1.28; //10%-critical value from the standard normal distribution
alpha_X(1) = 0.01; //define the AR coefficients
alpha_X(2) = 0.5;
alpha_X(3) = -0.2;
alpha_X(4) = -0.1;
alpha_X(5) = 0.2;
alpha_X(6) = 0.1;
alpha_Y(1) = 0.04;
alpha_Y(2) = 0.7;
alpha_Y(3) = -0.1;
alpha_Y(4) = -0.3;
alpha_Y(5) = 0.1;
alpha_Y(6) = 0.1;
NL_Dgp::gen_RANV<NL_Dgp::gen_SN> (epsilon_t, eta_t, delta, 0., 0, 13435); //generate skewed-normal random errors
NL_Dgp::gen_RANV<NL_Dgp::gen_SN> (epsilon_s, eta_s, delta, 0., 0, 53435);
/************************************************************ Using the Bartlett kernel ***********************************************************************/
output_filename = "./Results/NonGaussian/SN/file_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_bartlett_kernel_univariate.txt";
size_filename = "./Results/NonGaussian/SN/size_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_bartlett_kernel_univariate.txt";
power_filename = "./Results/NonGaussian/SN/power_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_bartlett_kernel_univariate.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 << "Lag smooth length = " << lag_smooth << endl;
//calculate 5%- and 10%- asymptotic sizes and empirical critical values
NGPower::cValue<bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (asymp_REJF, empir_CV, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s,
delta, expn, asymp_CV, seed, size_out);
output << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
cout << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 1; //nonzero correlation
NGPower::power_f<bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 2; //zero correlation
NGPower::power_f<bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 3; //dependence
NGPower::power_f<bartlett_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output.close();
size_out.close();
pwr_out.close();
/************************************************************ Using the Daniell kernel ***********************************************************************/
output_filename = "./Results/NonGaussian/SN/file_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_daniell_kernel_univariate.txt";
size_filename = "./Results/NonGaussian/SN/size_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_daniell_kernel_univariate.txt";
power_filename = "./Results/NonGaussian/SN/power_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_daniell_kernel_univariate.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 << "Lag smooth length = " << lag_smooth << endl;
//calculate 5%- and 10%- asymptotic sizes and empirical critical values
NGPower::cValue<daniell_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (asymp_REJF, empir_CV, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s,
delta, expn, asymp_CV, seed, size_out);
output << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
cout << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 1; //nonzero correlation
NGPower::power_f<daniell_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 2; //zero correlation
NGPower::power_f<daniell_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 3; //dependence
NGPower::power_f<daniell_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output.close();
size_out.close();
pwr_out.close();
/************************************************************ Using the QS kernel ***********************************************************************/
output_filename = "./Results/NonGaussian/SN/file_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_QS_kernel_univariate.txt";
size_filename = "./Results/NonGaussian/SN/size_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_QS_kernel_univariate.txt";
power_filename = "./Results/NonGaussian/SN/power_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_QS_kernel_univariate.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 << "Lag smooth length = " << lag_smooth << endl;
//calculate 5%- and 10%- asymptotic sizes and empirical critical values
NGPower::cValue<QS_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (asymp_REJF, empir_CV, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s,
delta, expn, asymp_CV, seed, size_out);
output << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
cout << "5%- and 10%- empirical critical values for lag_smooth = " << lag_smooth << ": " << "(" << empir_CV(1) << " , " << empir_CV(2) << ")" << endl;
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 1; //nonzero correlation
NGPower::power_f<QS_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 2; //zero correlation
NGPower::power_f<QS_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
choose_alt = 3; //dependence
NGPower::power_f<QS_kernel, NL_Dgp::gen_Bilinear<NL_Dgp::gen_SN>, NGReg::cmean_BL, NL_Dgp::est_BL> (empir_REJF, asymp_REJF, number_sampl, T, TL, lag_smooth,
alpha_X, alpha_Y, epsilon_t, epsilon_s, eta_t, eta_s, delta,
rho, expn, empir_CV, asymp_CV, choose_alt, seed, pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
output << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << empir_REJF(1) << " , " << empir_REJF(2) << ")" << endl;
cout << "5%- and 10% - asymptotic rejection rates for choose_alt = " << choose_alt << ": " << "(" << asymp_REJF(1) << " , " << asymp_REJF(2) << ")" << endl;
output.close();
size_out.close();
pwr_out.close();
/***************************************** Finish the Simulations for the Proposed Test: The Univariate Case ************************************************/
/************************************************************************************************************************************************************/
#endif //end comment
#if 0 //begin comment
/**************************************************** Start the Simulations for El Himdi & Roy's test: The Bivariate Case ***********************************/
/************************************************************************************************************************************************************/
int T = 100;
int number_sampl = 500;
Matrix alpha(3,1), beta(3,1), lambda(3,1), sigma(2,1);
alpha(1) = 0.01;
alpha(2) = 0.04;
alpha(3) = 0.02;
beta(1) = 0.7;
beta(2) = 0.4;
beta(3) = -0.5;
lambda(1) = 0.;
lambda(2) = -1;
lambda(3) = -0.8;
sigma(1) = 1.5; // cf. Dgp::gen_CAR1 in dgp.h
sigma(2) = 1.5; // cf. Dgp::gen_CAR1 in dgp.h
//double rho = 0.2, threshold = 1.54; //set threshold equal to 1.54 for zero correlation
double rho = 0.2, corr = 0.8; //set the correlation betwen X and Y1 to 0.8
unsigned long seed = 856764325;
string output_filename, size_filename, power_filename;
ofstream output, size_out, pwr_out;
Dep_tests dep_obj;
Matrix cv(2, 1), asymp_cv(2, 1), empir_REJF(2, 1), asymp_REJF(2, 1);
int lag_smooth = 5;
output_filename = "./Results/HimdiRoy/file_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_corr="
+ boost::lexical_cast<std::string>(corr) + "_bivariate_corr.txt";
size_filename = "./Results/HimdiRoy/size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_corr="
+ boost::lexical_cast<std::string>(corr) + "_bivariate_corr.txt";