Preface xi
1. Financial Time Series and Their Characteristics 1
1.1 Asset Returns, 2
1.2 Distributional Properties of Returns, 6
1.3 Processes Considered, 17
2. Linear Time Series Analysis and Its Applications 22
2.1 Stationarity, 23
2.2 Correlation and Autocorrelation Function, 23
2.3 White Noise and Linear Time Series, 26
2.4 Simple Autoregressive Models, 28
2.5 Simple Moving-Average Models, 42
2.6 Simple ARMA Models, 48
2.7 Unit-Root Nonstationarity, 56
2.8 Seasonal Models, 61
2.9 Regression Models with Time Series Errors, 66
2.10 Long-Memory Models, 72
Appendix A. Some SCA Commands, 74
3. Conditional Heteroscedastic Models 79
3.1 Characteristics of Volatility, 80
3.2 Structure of a Model, 81
3.3 The ARCH Model, 82
3.4 The GARCH Model, 93
3.5 The Integrated GARCH Model, 100
3.6 The GARCH-M Model, 101
3.7 The Exponential GARCH Model, 102
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viii CONTENTS
3.8 The CHARMA Model, 107
3.9 Random Coefficient Autoregressive Models, 109
3.10 The Stochastic Volatility Model, 110
3.11 The Long-Memory Stochastic Volatility Model, 110
3.12 An Alternative Approach, 112
3.13 Application, 114
3.14 Kurtosis of GARCH Models, 118
Appendix A. Some RATS Programs for Estimating Volatility
Models, 120
4. Nonlinear Models and Their Applications 126
4.1 Nonlinear Models, 128
4.2 Nonlinearity Tests, 152
4.3 Modeling, 161
4.4 Forecasting, 161
4.5 Application, 164
Appendix A. Some RATS Programs for Nonlinear Volatility
Models, 168
Appendix B. S-Plus Commands for Neural Network, 169
5. High-Frequency Data Analysis and Market Microstructure 175
5.1 Nonsynchronous Trading, 176
5.2 Bid-Ask Spread, 179
5.3 Empirical Characteristics of Transactions Data, 181
5.4 Models for Price Changes, 187
5.5 Duration Models, 194
5.6 Nonlinear Duration Models, 206
5.7 Bivariate Models for Price Change and Duration, 207
Appendix A. Review of Some Probability Distributions, 212
Appendix B. Hazard Function, 215
Appendix C. Some RATS Programs for Duration Models, 216
6. Continuous-Time Models and Their Applications 221
6.1 Options, 222
6.2 Some Continuous-Time Stochastic Processes, 222
6.3 Ito’s Lemma, 226
6.4 Distributions of Stock Prices and Log Returns, 231
6.5 Derivation of Black–Scholes Differential Equation, 232
CONTENTS ix
6.6 Black–Scholes Pricing Formulas, 234
6.7 An Extension of Ito’s Lemma, 240
6.8 Stochastic Integral, 242
6.9 Jump Diffusion Models, 244
6.10 Estimation of Continuous-Time Models, 251
Appendix A. Integration of Black–Scholes Formula, 251
Appendix B. Approximation to Standard Normal Probability, 253
7. Extreme Values, Quantile Estimation, and Value at Risk 256
7.1 Value at Risk, 256
7.2 RiskMetrics, 259
7.3 An Econometric Approach to VaR Calculation, 262
7.4 Quantile Estimation, 267
7.5 Extreme Value Theory, 270
7.6 An Extreme Value Approach to VaR, 279
7.7 A New Approach Based on the Extreme Value Theory, 284
8. Multivariate Time Series Analysis and Its Applications 299
8.1 Weak Stationarity and Cross-Correlation Matrixes, 300
8.2 Vector Autoregressive Models, 309
8.3 Vector Moving-Average Models, 318
8.4 Vector ARMA Models, 322
8.5 Unit-Root Nonstationarity and Co-Integration, 328
8.6 Threshold Co-Integration and Arbitrage, 332
8.7 Principal Component Analysis, 335
8.8 Factor Analysis, 341
Appendix A. Review of Vectors and Matrixes, 348
Appendix B. Multivariate Normal Distributions, 353
9. Multivariate Volatility Models and Their Applications 357
9.1 Reparameterization, 358
9.2 GARCH Models for Bivariate Returns, 363
9.3 Higher Dimensional Volatility Models, 376
9.4 Factor-Volatility Models, 383
9.5 Application, 385
9.6 Multivariate t Distribution, 387
Appendix A. Some Remarks on Estimation, 388
x CONTENTS
10. Markov Chain Monte Carlo Methods with Applications 395
10.1 Markov Chain Simulation, 396
10.2 Gibbs Sampling, 397
10.3 Bayesian Inference, 399
10.4 Alternative Algorithms, 403
10.5 Linear Regression with Time-Series Errors, 406
10.6 Missing Values and Outliers, 410
10.7 Stochastic Volatility Models, 418
10.8 Markov Switching Models, 429
10.9 Forecasting, 438
10.10 Other Applications, 441
Index 445