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