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Analysis of Financial Time Series
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Table of Contents

Preface xvii Preface to the Second Edition xix Preface to the First Edition xxi 1 Financial Time Series and Their Characteristics 1 1.1 Asset Returns, 2 1.2 Distributional Properties of Returns, 7 1.3 Processes Considered, 22 2 Linear Time Series Analysis and Its Applications 29 2.1 Stationarity, 30 2.2 Correlation and Autocorrelation Function, 30 2.3 White Noise and Linear Time Series, 36 2.4 Simple AR Models, 37 2.5 Simple MA Models, 57 2.6 Simple ARMA Models, 64 2.7 Unit-Root Nonstationarity, 71 2.8 Seasonal Models, 81 2.9 Regression Models with Time Series Errors, 90 2.10 Consistent Covariance Matrix Estimation, 97 2.11 Long-Memory Models, 101 3 Conditional Heteroscedastic Models 109 3.1 Characteristics of Volatility, 110 3.2 Structure of a Model, 111 3.3 Model Building, 113 3.4 The ARCH Model, 115 3.5 The GARCH Model, 131 3.6 The Integrated GARCH Model, 140 3.7 The GARCH-M Model, 142 3.8 The Exponential GARCH Model, 143 3.9 The Threshold GARCH Model, 149 3.10 The CHARMA Model, 150 3.11 Random Coefficient Autoregressive Models, 152 3.12 Stochastic Volatility Model, 153 3.13 Long-Memory Stochastic Volatility Model, 154 3.14 Application, 155 3.15 Alternative Approaches, 159 3.16 Kurtosis of GARCH Models, 165 4 Nonlinear Models and Their Applications 175 4.1 Nonlinear Models, 177 4.2 Nonlinearity Tests, 205 4.3 Modeling, 214 4.4 Forecasting, 215 4.5 Application, 218 5 High-Frequency Data Analysis and Market Microstructure 231 5.1 Nonsynchronous Trading, 232 5.2 Bid?Ask Spread, 235 5.3 Empirical Characteristics of Transactions Data, 237 5.4 Models for Price Changes, 244 5.5 Duration Models, 253 5.6 Nonlinear Duration Models, 264 5.7 Bivariate Models for Price Change and Duration, 265 5.8 Application, 270 6 Continuous-Time Models and Their Applications 287 6.1 Options, 288 6.2 Some Continuous-Time Stochastic Processes, 288 6.3 Ito's Lemma, 292 6.4 Distributions of Stock Prices and Log Returns, 297 6.5 Derivation of Black?Scholes Differential Equation, 298 6.6 Black?Scholes Pricing Formulas, 300 6.7 Extension of Ito's Lemma, 309 6.8 Stochastic Integral, 310 6.9 Jump Diffusion Models, 311 6.10 Estimation of Continuous-Time Models, 318 7 Extreme Values, Quantiles, and Value at Risk 325 7.1 Value at Risk, 326 7.2 RiskMetrics, 328 7.3 Econometric Approach to VaR Calculation, 333 7.4 Quantile Estimation, 338 7.5 Extreme Value Theory, 342 7.6 Extreme Value Approach to VaR, 353 7.7 New Approach Based on the Extreme Value Theory, 359 7.8 The Extremal Index, 377 8 Multivariate Time Series Analysis and Its Applications 389 8.1 Weak Stationarity and Cross-Correlation Matrices, 390 8.2 Vector Autoregressive Models, 399 8.3 Vector Moving-Average Models, 417 8.4 Vector ARMA Models, 422 8.5 Unit-Root Nonstationarity and Cointegration, 428 8.6 Cointegrated VAR Models, 432 8.7 Threshold Cointegration and Arbitrage, 442 8.8 Pairs Trading, 446 9 Principal Component Analysis and Factor Models 467 9.1 A Factor Model, 468 9.2 Macroeconometric Factor Models, 470 9.3 Fundamental Factor Models, 476 9.4 Principal Component Analysis, 483 9.5 Statistical Factor Analysis, 489 9.6 Asymptotic Principal Component Analysis, 498 10 Multivariate Volatility Models and Their Applications 505 10.1 Exponentially Weighted Estimate, 506 10.2 Some Multivariate GARCH Models, 510 10.3 Reparameterization, 516 10.4 GARCH Models for Bivariate Returns, 521 10.5 Higher Dimensional Volatility Models, 537 10.6 Factor?Volatility Models, 543 10.7 Application, 546 10.8 Multivariate t Distribution, 548 11 State-Space Models and Kalman Filter 557 11.1 Local Trend Model, 558 11.2 Linear State-Space Models, 576 11.3 Model Transformation, 577 11.4 Kalman Filter and Smoothing, 591 11.5 Missing Values, 600 11.6 Forecasting, 601 11.7 Application, 602 12 Markov Chain Monte Carlo Methods with Applications 613 12.1 Markov Chain Simulation, 614 12.2 Gibbs Sampling, 615 12.3 Bayesian Inference, 617 12.4 Alternative Algorithms, 622 12.5 Linear Regression with Time Series Errors, 624 12.6 Missing Values and Outliers, 628 12.7 Stochastic Volatility Models, 636 12.8 New Approach to SV Estimation, 649 12.9 Markov Switching Models, 660 12.10 Forecasting, 666 12.11 Other Applications, 669 Exercises, 670 References, 671 Index 673

About the Author

RUEY S. TSAY, PhD, is H. G. B. Alexander Professor of Econometrics and Statistics at the University of Chicago Booth School of Business. Dr. Tsay has written over 100 published articles in the areas of business and economic forecasting, data analysis, risk management, and process control, and he is the coauthor of A Course in Time Series Analysis (Wiley). Dr. Tsay is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, the Royal Statistical Society, and Academia Sinica.

Reviews

"Analysis of financial time series, third edition, is an ideal book for introductory courses on time series at the graduate level and a valuable supplement for statistics courses in time series at the upper-undergraduate level." ( Mathematical Reviews, 2011) "Nevertheless, all in all the book can be a very useful reference for students as well as for professionals." (Zentralblatt MATH, 2011) "Factor models, an important technique used in quantitative finance, are given a full treatment with macroeconomic factor models and fundamental factor models. The coverage of the book is comprehensive. It starts from basic time series techniques and finishes with advanced concepts such as state space models and MCMC methods. There is a balance between the theoretical background necessary to appreciate the nuances and the practical aspect of implementation. More importantly it gives insights about what time series models can't address. The book has an excellent supporting website which has all the programs and data sets which helps to internalize the concepts. Finally, teaching professionals should find the solutions manual as a valuable tool to explain concepts and to ensure understanding." (BookPleasures.com, January 2011) "This book provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described." (Insurance News Net, 8 December 2010)

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