GARCH models: structure, statistical inference and financial applications
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Chichester [u.a.]
Wiley
2010
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Franz. übers. |
| Physical Description: | XIV, 489 S. graph. Darst. |
| ISBN: | 9780470683910 |
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MARC
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| adam_text | Titel: GARCH models
Autor: Francq, Christian
Jahr: 2010
Contents
Preface xi
Notation xiii
1 Classical Time Series Models and Financial Series 1
1.1 Stationary Processes 1
1.2 ARMA and ARIMA Models 3
1.3 Financial Series 7
1.4 Random Variance Models 10
1.5 Bibliographical Notes 12
1.6 Exercises 12
Part I Univariate GARCH Models 17
2 GARCH(p, q) Processes 19
2.1 Definitions and Representations 19
2.2 Stationarity Study 24
2.2.1 The GARCH(1, 1) Case 24
2.2.2 The General Case 28
2.3 ARCH (oo) Representation* 39
2.3.1 Existence Conditions 39
2.3.2 ARCH (oo) Representation of a GARCH 42
2.3.3 Long-Memory ARCH 43
2.4 Properties of the Marginal Distribution 45
2.4.1 Even-Order Moments 45
2.4.2 Kurtosis 48
2.5 Autocovariances of the Squares of a GARCH 50
2.5.1 Positivity of the Autocovariances 50
2.5.2 The Autocovariances Do Not Always Decrease 51
2.5.3 Explicit Computation of the Autocovariances of the Squares 52
2.6 Theoretical Predictions 53
2.7 Bibliographical Notes 57
2.8 Exercises 58
3 Mixing* 63
3.1 Markov Chains with Continuous State Space 63
3.2 Mixing Properties of GARCH Processes 68
3.3 Bibliographical Notes 76
3.4 Exercises 76
4 Temporal Aggregation and Weak GARCH Models 79
4.1 Temporal Aggregation of GARCH Processes 79
4.1.1 Nontemporal Aggregation of Strong Models 80
4.1.2 Nonaggregation in the Class of Semi-Strong GARCH Processes 81
4.2 Weak GARCH 82
4.3 Aggregation of Strong GARCH Processes in the Weak GARCH Class 85
4.4 Bibliographical Notes 88
4.5 Exercises 89
Part II Statistical Inference 91
5 Identification 93
5.1 Autocorrelation Check for White Noise 93
5.1.1 Behavior of the Sample Autocorrelations of a GARCH Process 94
5.1.2 Portmanteau Tests 97
5.1.3 Sample Partial Autocorrelations of a GARCH 97
5.1.4 Numerical Illustrations 98
5.2 Identifying the ARMA Orders of an ARMA-GARCH 100
5.2.1 Sample Autocorrelations of an ARMA-GARCH 101
5.2.2 Sample Autocorrelations of an ARMA-GARCH Process When the Noise
is Not Symmetrically Distributed 104
5.2.3 Identifying the Orders (P, Q) 106
5.3 Identifying the GARCH Orders of an ARMA-GARCH Model 108
5.3.1 Corner Method in the GARCH Case 109
5.3.2 Applications 109
5.4 Lagrange Multiplier Test for Conditional Homoscedasticity 111
5.4.1 General Form of the LM Test 111
5.4.2 LM Test for Conditional Homoscedasticity 115
5.5 Application to Real Series 117
5.6 Bibliographical Notes 120
5.7 Exercises 122
6 Estimating ARCH Models by Least Squares 127
6.1 Estimation of ARCH(^r) models by Ordinary Least Squares 127
6.2 Estimation of ARCH( ?) Models by Feasible Generalized Least Squares 132
6.3 Estimation by Constrained Ordinary Least Squares 135
6.3.1 Properties of the Constrained OLS Estimator 135
6.3.2 Computation of the Constrained OLS Estimator 137
6.4 Bibliographical Notes 138
6.5 Exercises 138
7 Estimating GARCH Models by Quasi-Maximum Likelihood 141
7.1 Conditional Quasi-Likelihood 141
7.1.1 Asymptotic Properties of the QMLE 143
7.1.2 The ARCH(l) Case: Numerical Evaluation of the Asymptotic Variance 147
7.1.3 The Nonstationary ARCH(l) 148
7.2 Estimation of ARMA-GARCH Models by Quasi-Maximum Likelihood 150
7.3 Application to Real Data 155
7.4 Proofs of the Asymptotic Results* 156
7.5 Bibliographical Notes 180
7.6 Exercises 180
8 Tests Based on the Likelihood 185
8.1 Test of the Second-Order Stationarity Assumption 186
8.2 Asymptotic Distribution of the QML When 90 is at the Boundary 187
8.2.1 Computation of the Asymptotic Distribution 191
8.3 Significance of the GARCH Coefficients 194
8.3.1 Tests and Rejection Regions 194
8.3.2 Modification of the Standard Tests 196
8.3.3 Test for the Nullity of One Coëfficiënt 197
8.3.4 Conditional Homoscedasticity Tests with ARCH Models 199
8.3.5 Asymptotic Comparison of the Tests 201
8.4 Diagnostic Checking with Portmanteau Tests 204
8.5 Application: Is the GARCH( 1,1) Model Overrepresented? 204
8.6 Proofs of the Main Results* 207
8.7 Bibliographical Notes 215
8.8 Exercises 215
9 Optimal Inference and Altematives to the QMLE* 219
9.1 Maximum Likelihood Estimator 219
9.1.1 Asymptotic Behavior 220
9.1.2 One-Step Efficiënt Estimator 222
9.1.3 Semiparametric Models and Adaptive Estimators 223
9.1.4 Local Asymptotic Normality 226
9.2 Maximum Likelihood Estimator with Misspecified Density 231
9.2.1 Condition for the Convergence of § ,/, to Oo 231
9.2.2 Reparameterization Implying the Convergence of 0 j, to ö0 232
9.2.3 Choice of Instrumental Density h 233
9.2.4 Asymptotic Distribution of ên,h 234
9.3 Alternative Estimation Methods 236
9.3.1 Weighted LSE for the ARMA Parameters 236
9.3.2 Self-Weighted QMLE 237
9.3.3 Lp Estimators 237
9.3.4 Least Absolute Value Estimation 238
9.3.5 Whittle Estimator 238
9.4 Bibliographical Notes 239
9.5 Exercises 239
Part III Extensions and Applications 243
10 Asymmetries 245
10.1 Exponential GARCH Model 246
10.2 Threshold GARCH Model 250
10.3 Asymmetrie Power GARCH Model 256
10.4 Other Asymmetrie GARCH Models 258
10.5 A GARCH Model with Contemporaneous Conditional Asymmetry 259
10.6 Empirical Comparisons of Asymmetrie GARCH Formulations 261
10.7 Bibliographical Notes 269
10.8 Exercises 270
11 Multivariate GARCH Processes 273
11.1 Multivariate Stationary Processes 273
11.2 Multivariate GARCH Models 275
11.2.1 Diagonal Model 276
11.2.2 Vector GARCH Model 277
11.2.3 Constant Conditional Correlations Models 279
11.2.4 Dynamic Conditional Correlations Models 281
11.2.5 BEKK-GARCH Model 281
11.2.6 Factor GARCH Models 284
11.3 Stationarity 286
11.3.1 Stationarity of VEC and BEKK Models 286
11.3.2 Stationarity of the CCC Model 289
11.4 Estimation of the CCC Model 291
11.4.1 Identifiability Conditions 292
11.4.2 Asymptotic Properties of the QMLE of the CCC-GARCH model 294
11.4.3 Proof of the Consistency and the Asymptotic Normality of the QML 296
11.5 Bibliographical Notes 307
11.6 Exercises 308
12 Financial Applications 311
12.1 Relation between GARCH and Continuous-Time Models 311
12.1.1 Some Properties of Stochastic Differential Equations 311
12.1.2 Convergence of Markov Chains to Diffusions 313
12.2 Option Pricing 319
12.2.1 Derivatives and Options 319
12.2.2 The Black-Scholes Approach 319
12.2.3 Historie Volatility and Implied Volatilities 321
12.2.4 Option Pricing when the Underlying Process is a GARCH 321
12.3 Value at Risk and Other Risk Measures 327
12.3.1 Value at Risk 327
12.3.2 Other Risk Measures 331
12.3.3 Estimation Methods 334
12.4 Bibliographical Notes 337
12.5 Exercises 338
Part IV Appendices 341
A Ergodicity, Martingales, Mixing 343
A. 1 Ergodicity 343
A.2 Martingale Increments 344
A.3 Mixing 347
A.3.1 a-Mixing and ^-Mixing Coefficients 348
A.3.2 Covariance Inequality 349
A.3.3 Central Limit Theorem 352
B Autocorrelation and Partial Autocorrelation 353
B.l Partial Autocorrelation 353
B.2 Generalized Bartlett Formula for Nonlinear Processes 359
Solutions to the Exercises
Problems 439
References 473
Index 487
|
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| edition | 1. publ. |
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| indexdate | 2024-07-09T22:44:25Z |
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| isbn | 9780470683910 |
| language | English French |
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| spelling | Francq, Christian 1962- Verfasser (DE-588)171416821 aut Models GARCH GARCH models structure, statistical inference and financial applications Christian Francq ; Jean-Michel Zakoian 1. publ. Chichester [u.a.] Wiley 2010 XIV, 489 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Franz. übers. Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf GARCH-Prozess (DE-588)4346436-1 gnd rswk-swf Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Finance--Mathematical models. Zeitreihenanalyse (DE-588)4067486-1 s Kreditmarkt (DE-588)4073788-3 s GARCH-Prozess (DE-588)4346436-1 s Inferenzstatistik (DE-588)4247120-5 s DE-604 Zakoïan, Jean-Michel 1962- Verfasser (DE-588)17110482X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020543137&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Francq, Christian 1962- Zakoïan, Jean-Michel 1962- GARCH models structure, statistical inference and financial applications Zeitreihenanalyse (DE-588)4067486-1 gnd Inferenzstatistik (DE-588)4247120-5 gnd GARCH-Prozess (DE-588)4346436-1 gnd Kreditmarkt (DE-588)4073788-3 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4247120-5 (DE-588)4346436-1 (DE-588)4073788-3 |
| title | GARCH models structure, statistical inference and financial applications |
| title_alt | Models GARCH |
| title_auth | GARCH models structure, statistical inference and financial applications |
| title_exact_search | GARCH models structure, statistical inference and financial applications |
| title_full | GARCH models structure, statistical inference and financial applications Christian Francq ; Jean-Michel Zakoian |
| title_fullStr | GARCH models structure, statistical inference and financial applications Christian Francq ; Jean-Michel Zakoian |
| title_full_unstemmed | GARCH models structure, statistical inference and financial applications Christian Francq ; Jean-Michel Zakoian |
| title_short | GARCH models |
| title_sort | garch models structure statistical inference and financial applications |
| title_sub | structure, statistical inference and financial applications |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Inferenzstatistik (DE-588)4247120-5 gnd GARCH-Prozess (DE-588)4346436-1 gnd Kreditmarkt (DE-588)4073788-3 gnd |
| topic_facet | Zeitreihenanalyse Inferenzstatistik GARCH-Prozess Kreditmarkt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020543137&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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