1. Volatility Models 1
1.1 Introduction 1
1.2 GARCH 1
1.3 Stochastic Volatility 31
1.4 Realized Volatility 42
Part I. ARCH and SV
2. Nonlinear ARCH Models 63
2.1 Introduction 63
2.2 Standard GARCH model 64
2.3 Predecessors to Nonlinear GARCH 65
2.4 Nonlinear ARCH and GARCH 67
2.5 Testing 76
2.6 Estimation 81
2.7 Forecasting 83
2.8 Multiplicative Decomposition 86
2.9 Conclusion 88
3. Mixture and Regime-switching GARCH Models 89
3.1 Introduction 89
3.2 Regime-switching GARCH models 92
3.3 Stationarity and Moment Structure 102
3.4 Regime Inference, Likelihood Functions, and Volatility Forecasting 111
3.5 Application of Mixture GARCH Models 119
3.6 Conclusion 124
4. Forecasting High Dimensional Covariance Matrices 129
4.1 Introduction 129
4.2 Notation 130
4.3 Rolling-Window Forecasts 131
4.4 Dynamic Models 136
4.5 High-Frequency Based Forecasts 147
4.6 Forecast Evaluation 154
4.7 Conclusion 157
5. Mean, Volatility and Skewness Spillovers in Equity Markets 159
5.1 Introduction 159
5.2 Data and Summary Statistics 162
5.3 Empirical Results 171
5.4 Conclusion 177
6. Relating Stochastic Volatility Estimation Methods 185
6.1 Introduction 185
6.2 Theory and Methodology 188
6.3 Comparison of Methods 201
6.4 Estimating Volatility Models in Practice 209
6.5 Conclusion 217
7. Multivariate Stochastic Volatility Models 221
7.1 Introduction 221
7.2 MSV model 223
7.3 Factor MSV model 231
7.4 Applications to Stock Indices Returns 237
7.5 Conclusion 244
8. Model Selection and Testing of Volatility Models 249
8.1 Introduction 249
8.2 Model Selection and Testing 252
8.3 Empirical Example 265
8.4 Conclusion 277
Part II. Other models and methods
9. Multiplicative Error Models 281
9.1 Introduction 281
9.2 Theory and Methodology 283
9.3 MEM Application 293
9.4 MEM Extensions 302
9.5 Conclusion 308
10. Locally Stationary Volatility Modeling 311
10.1 Introduction 311
10.2 Empirical evidences 314
10.3 Locally Stationary Processes 319
10.4 Locally Stationary Volatility Models 323
10.5 Multivariate Models for Locally Stationary Volatility 331
10.6 Conclusion 333
11. Nonparametric and Semiparametric Volatility Models 335
11.1 Introduction 335
11.2 Nonparametric and Semiparametric Univariate Models 338
11.3 Nonparametric and Semiparametric Multivariate Volatility Models 354
11.4 Empirical Analysis 360
11.5 Conclusion 363
12. Copula-based Volatility Models 367
12.1 Introduction 367
12.2 Definition and Properties of Copulas 369
12.3 Estimation 375
12.4 Dynamic Copulas 381
12.5 Value-at-Risk 387
12.6 Multivariate Static copulas 389
12.7 Conclusion 395
Part III. Realized Volatility
13. Realized Volatility: Theory and Applications 399
13.1 Introduction 399
13.2 Modelling Framework 400
13.3 Issues in Handling Intra-day Transaction Databases 404
13.4 Realized Variance and Covariance 411
14.5 Modelling and Forecasting 422
13.6 Asset Pricing 426
13.7 Estimating Continuous Time Models 431
14. Likelihood-Based Volatility Estimators 435
14.1 Introduction 435
14.2 Volatility Estimation 438
14.3 Covariance Estimation 447
14.4 Empirical Application 450
14.5 Conclusion 452
15. HAR Modeling for Realized Volatility Forecasting 453
15.1 Introduction 453
15.2 Stylized Facts 455
15.3 Heterogeneity and Volatility Persistence 457
15.4 HAR Extensions 463
15.5 Multivariate Models 469
15.6 Applications 473
15.7 Conclusion 478
16. Forecasting volatility with MIDAS 481
16.1 Introduction 481
16.2 MIDAS Regression Models and Volatility Forecasting 482
16.3 Likelihood-based Methods 492
16.4 Multivariate Models 505
16.5 Conclusion 507
17. Jumps 509
17.1 Introduction 509
17.2 Estimators of Integrated Variance and Integrated Covariance 519
17.3 Testing for the Presence of Jumps 548
17.4 Conclusion 563
18. Jumps, Periodicity and Microstructure Noise 565
18.1 Introduction 565
18.2 Model 568
18.3 Price Jump Detection Method 570
18.4 Simulation Study 576
18.5 Comparison on NYSE-Stock Prices 581
18.6 Conclusion 583
19. Volatility Forecasts Evaluation and Comparison 585
19.1 Introduction 585
19.2 Notation 588
19.3 Single Forecast Evaluation 590
19.4 Loss Functions and the Latent Variable Problem 593
19.5 Pairwise Comparison 597
19.6 Multiple Comparison 601
19.7 Consistency of the Ordering and Inference on Forecast Performances 607
19.8 Conclusion 613
Index 615
Bibliography 629
