Analysis of Financial Time Series

1 Analysis of Financial time SeriesSecond EditionRUEY S. TSAYU niversity of ChicagoGraduate School of BusinessA JOHN WILEY & SONS, INC., PUBLICATIONA nalysis of Financial time SeriesWILEY Series IN PROBABILITY AND STATISTICSE stablished by WALTER A. SHEWHART and SAMUEL S. WILKSE ditors:David J. Balding, Noel A. C. Cressie, Nicholas I. Fisher,Iain M. Johnstone, J. B. Kadane, Geert Molenberghs, Louise M. Ryan,David W. Scott, Adrian F. M. Smith, Jozef L. TeugelsEditors Emeriti:Vic Barnett, J. Stuart Hunter, David G. KendallA complete list of the titles in this Series appears at the end of this of Financial time SeriesSecond EditionRUEY S. TSAYU niversity of ChicagoGraduate School of BusinessA JOHN WILEY & SONS, INC., PUBLICATIONC opyright 2005 by John Wiley & Sons, Inc. All rights by John Wiley & Sons, Inc.

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4 , 1951 Analysis of Financial time Series /Ruey S. Tsay. 2nd cm. Wiley-Interscience. Includes bibliographical references and 978-0-471-69074-0 ISBN-10 0-471-69074-0 (cloth)1. time - Series Analysis . 2. Econometrics. 3. Risk management. I..01 51955 dc222005047030 Printed in the United States of my parents and TeresaContentsPrefacexviiPreface to First Editionxix1. Financial time Series and Their Asset Returns, Distributional Properties of Returns, Review of Statistical Distributions and Their Moments, Distributions of Returns, Multivariate Returns, Likelihood Function of Returns, Empirical Properties of Returns, Processes Considered, 20 Exercises, 22 References, 232. Linear time Series Analysis and Its Stationarity, Correlation and Autocorrelation Function, White Noise and Linear time Series , Simple Autoregressive Models, Properties of AR Models, Identifying AR Models in Practice, Goodness of Fit, Forecasting, Simple Moving-Average Models, Properties of MA Models, Identifying MA Order, Estimation, Forecasting Using MA Models, Simple ARMA Models, Properties of ARMA(1,1)

5 Models, General ARMA Models, Identifying ARMA Models, Forecasting Using an ARMA Model, Three Model Representations for an ARMA Model, Unit-Root Nonstationarity, Random Walk, Random Walk with Drift, Trend-Stationary time Series , General Unit-Root Nonstationary Models, Unit-Root Test, Seasonal Models, Seasonal Differencing, Multiplicative Seasonal Models, regression Models with time Series Errors, Consistent Covariance Matrix Estimation, Long-Memory Models, 89 Appendix: Some SCA Commands, 91 Exercises, 93 References, 963. Conditional Heteroscedastic Characteristics of Volatility, Structure of a Model, Model Building, Testing for ARCH Effect, The ARCH Model, Properties of ARCH Models, Weaknesses of ARCH Models, Building an ARCH Model, Some Examples, The GARCH Model, An Illustrative Example, Forecasting Evaluation, A Two-Pass Estimation Method, The Integrated GARCH Model, The GARCH-M Model, The Exponential GARCH Model, An Alternative Model Form, An Illustrative Example, Second Example, Forecasting Using an EGARCH Model, The Threshold GARCH Model, The CHARMA Model, Effects of Explanatory Variables, Random Coefficient Autoregressive Models, The Stochastic Volatility Model, The Long-Memory Stochastic Volatility Model.

6 Application, Alternative Approaches, Use of High-Frequency Data, Use of Daily Open, High, Low, and Close Prices, Kurtosis of GARCH Models, 145 Appendix: Some RATS Programs for Estimating Volatility Models, 147 Exercises, 148 References, 1514. Nonlinear Models and Their Nonlinear Models, Bilinear Model, Threshold Autoregressive (TAR) Model, Smooth Transition AR (STAR) Model, Markov Switching Model, Nonparametric Methods, Functional Coefficient AR Model, Nonlinear Additive AR Model, Nonlinear State-Space Model, Neural Networks, Nonlinearity Tests, Nonparametric Tests, Parametric Tests, Applications, Modeling, Forecasting, Parametric Bootstrap, Forecasting Evaluation, Application, 194 Appendix A: Some RATS Programs for Nonlinear VolatilityModels, 199 Appendix B: S-Plus Commands for Neural Network, 200 Exercises, 200 References, 2025.

7 High-Frequency Data Analysis and Market Nonsynchronous Trading, Bid Ask Spread, Empirical Characteristics of Transactions Data, Models for Price Changes, Ordered Probit Model, A Decomposition Model, Duration Models, The ACD Model, Simulation, Estimation, Nonlinear Duration Models, Bivariate Models for Price Change and Duration, 237 Appendix A: Review of Some Probability Distributions, 242 Appendix B: Hazard Function, 245 Appendix C: Some RATS Programs for Duration Models, 246 Exercises, 248 References, 2506. Continuous- time Models and Their Options, Some Continuous- time Stochastic Processes, The Wiener Process, Generalized Wiener Processes, Ito Processes, Ito s Lemma, Review of Differentiation, Stochastic Differentiation, An Application, Estimation of and , Distributions of Stock Prices and Log Returns, Derivation of Black Scholes Differential Equation, Black Scholes Pricing Formulas, Risk-Neutral World, Formulas, Lower Bounds of European Options, Discussion, An Extension of Ito s Lemma, Stochastic Integral, Jump Diffusion Models, Option Pricing Under Jump Diffusion, Estimation of Continuous- time Models, 282 Appendix A: Integration of Black Scholes Formula, 282 Appendix B.

8 Approximation to Standard NormalProbability, 284 Exercises, 284 References, 2857. Extreme Values, quantile Estimation, and Value at Value at Risk, RiskMetrics, Discussion, Multiple Positions, An Econometric Approach to VaR Calculation, Multiple Periods, quantile Estimation, quantile and Order Statistics, quantile regression , Extreme Value Theory, Review of Extreme Value Theory, Empirical Estimation, Application to Stock Returns, Extreme Value Approach to VaR, Discussion, Multiperiod VaR, VaR for a Short Position, Return Level, A New Approach Based on the Extreme Value Theory, Statistical Theory, Mean Excess Function, A New Approach to Modeling Extreme Values, VaR Calculation Based on the New Approach, An Alternative Parameterization, Use of Explanatory Variables, Model Checking.

9 An Illustration, 330 Exercises, 335 References, 3378. Multivariate time Series Analysis and Its Weak Stationarity and Cross-Correlation Matrices, Cross-Correlation Matrices, Linear Dependence, Sample Cross-Correlation Matrices, Multivariate Portmanteau Tests, Vector Autoregressive Models, Reduced and Structural Forms, Stationarity Condition and Moments of a VAR(1)Model, Vector AR(p) Models, Building a VAR(p) Model, Impulse Response Function, Vector Moving-Average Models, Vector ARMA Models, Marginal Models of Components, Unit-Root Nonstationarity and Cointegration, An Error-Correction Form, Cointegrated VAR Models, Specification of the Deterministic Function, Maximum Likelihood Estimation, A Cointegration Test, Forecasting of Cointegrated VAR Models, An Example, Threshold Cointegration and Arbitrage, Multivariate Threshold Model, The Data, Estimation, 393 Appendix A: Review of Vectors and Matrices, 395 Appendix B: Multivariate Normal Distributions, 399 Appendix C: Some SCA Commands, 400 Exercises, 401 References, 4029.

10 Principal Component Analysis and Factor A Factor Model, Macroeconometric Factor Models, A Single-Factor Model, Multifactor Models, Fundamental Factor Models, BARRA Factor Model, Fama French Approach, Principal Component Analysis , Theory of PCA, Empirical PCA, Statistical Factor Analysis , Estimation, Factor Rotation, Applications, Asymptotic Principal Component Analysis , Selecting the Number of Factors, An Example, 437 Exercises, 440 References, 44110. Multivariate Volatility Models and Their Exponentially Weighted Estimate, Some Multivariate GARCH Models, Diagonal VEC Model, BEKK Model, Reparameterization, Use of Correlations, Cholesky Decomposition, GARCH Models for Bivariate Returns, Constant-Correlation Models, time -Varying Correlation Models, Some Recent Developments, Higher Dimensional Volatility Models, Factor Volatility Models, Application, MultivariatetDistribution, 482 Appendix: Some Remarks on Estimation, 483 Exercises, 488 References, 48911.