Bootstrap Tests for Regression Models Book

Preface xi

1 Tests for Linear Regression Models 1

1.1 Introduction 1

1.2 Tests for the classical linear regression model 1

1.3 Tests for linear regression models under weaker assumptions: random regressors and non-Normal IID errors 10

1.4 Tests for generalized linear regression models 14

1.4.1 HCCME-based tests 18

1.4.2 HAC-based tests 21

1.5 Finite-sample properties of asymptotic tests 25

1.5.1 Testing the significance of a subset of regressors 27

1.5.2 Testing for non-Normality of the errors 31

1.5.3 Using heteroskedasticity-robust tests of significance 33

1.6 Non-standard tests for linear regression models 35

1.7 Summary and concluding remarks 42

2 Simulation-based Tests: Basic Ideas 44

2.1 Introduction 44

2.2 Some key concepts and simple examples of tests for IID variables 46

2.2.1 Monte Carlo tests 47

2.2.2 Bootstrap tests 50

2.3 Simulation-based tests for regression models 55

2.3.1 The classical Normal model 55

2.3.2 Models with IID errors from an unspecified distribution 59

2.3.3 Dynamic regression models and bootstrap schemes 64

2.3.4 The choice of the number of artificial samples 67

2.4 Asymptotic properties of bootstrap tests 69

2.5 The double bootstrap 72

2.6 Summary and concluding remarks 77

3 Simulation-based Tests for Regression Models with IID Errors: Some Standard Cases 81

3.1 Introduction 81

3.2 A Monte Carlo test of the assumption of Normality 83

3.3 Simulation-based tests for heteroskedasticity 88

3.3.1 Monte Carlo tests for heteroskedasticity 91

3.3.2 Bootstrap tests for heteroskedasticity 94

3.3.3 Simulation experiments and tests for heteroskedasticity 95

3.4 Bootstrapping F tests oflinear coefficient restrictions 101

3.4.1 Regression models with strictly exogenous regressors 101

3.4.2 Stable dynamic regression models 109

3.4.3 Some simulation evidence concerning asymptotic and bootstrap F tests 110

3.5 Bootstrapping LM tests for serial correlation in dynamic regression models 118

3.5.1 Restricted or unrestricted estimates as parameters of bootstrap worlds 119

3.5.2 Some simulation evidence on the choice between restricted and unrestricted estimates 123

3.6 Summary and concluding remarks 132

4 Simulation-based Tests for Regression Models with IID Errors: Some Non-standard Cases 134

4.1 Introduction 134

4.2 Bootstrapping predictive tests 136

4.2.1 Asymptotic analysis for predictive test statistics 136

4.2.2 Single and double bootstraps for predictive tests 139

4.2.3 Simulation experiments and results 144

4.2.4 Dynamic regression models 148

4.3 Using bootstrap methods with a battery of OLS diagnostic tests 149

4.3.1 Regression models and diagnostic tests 151

4.3.2 Bootstrapping the minimum p-value of several diagnostic test statistics 152

4.3.3 Simulation experiments and results 155

4.4 Bootstrapping tests for structural breaks 160

4.4.1 Testing constant coefficients against an alternative with an unknown breakpoint 162

4.4.2 Simulation evidence for asymptotic and bootstrap tests 166

4.5 Summary and conclusions 173

5 Bootstrap Methods for Regression Models with Non-IID Errors 177

5.1 Introduction 177

5.2 Bootstrap methods for independent heteroskedastic errors 178

5.2.1 Model-based bootstraps 181

5.2.2 Pairs bootstraps 183

5.2.3 Wild bootstraps 185

5.2.4 Estimating function bootstraps 188

5.2.5 Bootstrapping dynamic regression models 190

5.3 Bootstrap methods for homoskedastic autocorrelated errors 193

5.3.1 Model-based bootstraps 194

5.3.2 Block bootstraps 198

5.3.3 Sieve bootstraps 201

5.3.4 Other methods 205

5.4 Bootstrap methods for heteroskedastic autocorrelated errors 207

5.4.1 Asymptotic theory tests 207

5.4.2 Block bootstraps 210

5.4.3 Other methods 213

5.5 Summary and concluding remarks 214

6 Simulation-based Tests for Regression Models with Non-IID Errors 218

6.1 Introduction 218

6.2 Bootstrapping heteroskedasticity-robust regression specification error tests 221

6.2.1 The forms of test statistics 221

6.2.2 Simulation experiments 226

6.3 Bootstrapping heteroskedasticity-robust autocorrelation tests for dynamic models 231

6.3.1 The forms of test statistics 232

6.3.2 Simulation experiments 235

6.4 Bootstrapping heteroskedasticity-robust structural break tests with an unknown breakpoint 241

6.5 Bootstrapping autocorrelation-robust Hausman tests 247

6.5.1 The forms of test statistics 247

6.5.2 Simulation experiments 254

6.6 Summary and conclusions 262

7 Simulation-based Tests for Non-nested Regression Models 266

7.1 Introduction 266

7.2 Asymptotic tests for models with non-nested regressors 268

7.2.1 Cox-type LLR tests 269

7.2.2 Artificial regression tests 273

7.2.3 Comprehensive model F-test 274

7.2.4 Regularity conditions and orthogonal regressors 274

7.2.5 Testing with multiple alternatives 275

7.2.6 Tests for model selection 277

7.2.7 Evidence from simulation experiments 279

7.3 Bootstrapping tests for models with non-nested regressors 281

7.3.1 One non-nested alternative regression model: significance levels 281

7.3.2 One non-nested alternative regression model: power 289

7.3.3 One non-nested alternative regression model: extreme cases 290

7.3.4 Two non-nested alternative regression models: significance levels 293

7.3.5 Two non-nested alternative regression models: power 295

7.4 Bootstrapping the LLR statistic with non-nested models 297

7.5 Summary and concluding remarks 300

8 Epilogue 303

Bibliography 305

Author Index 319

Subject Index 323