Analysis of Financial Time Series E-Book

Ruey S. Tsay

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 1011

Veröffentlichungsjahr: 2010

Beschreibung

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. The author begins with basic characteristics of financial time series data before covering three main topics: * Analysis and application of univariate financial time series * The return series of multiple assets * Bayesian inference in finance methods Key features of the new edition include additional coverage of modern day topics such as arbitrage, pair trading, realized volatility, and credit risk modeling; a smooth transition from S-Plus to R; and expanded empirical financial data sets. The overall objective of the book is to provide some knowledge of financial time series, introduce some statistical tools useful for analyzing these series and gain experience in financial applications of various econometric methods.

Leseprobe

Table of Contents

Series Page

Title Page

Copyright

Dedication

Preface

Preface to the Second Edition

Preface to the First Edition

Chapter 1: Financial Time Series and Their Characteristics

1.1 Asset Returns

1.2 Distributional Properties of Returns

1.3 Processes Considered

Appendix: R Packages

Chapter 2: Linear Time Series Analysis and Its Applications

2.1 Stationarity

2.2 Correlation and Autocorrelation Function

2.3 White Noise and Linear Time Series

2.4 Simple AR Models

2.5 Simple MA Models

2.6 Simple ARMA Models

2.7 Unit-Root Nonstationarity

2.8 Seasonal Models

2.9 Regression Models with Time Series Errors

2.10 Consistent Covariance Matrix Estimation

2.11 Long-Memory Models

Appendix: Some SCA Commands

Chapter 3: Conditional Heteroscedastic Models

3.1 Characteristics of Volatility

3.2 Structure of a Model

3.3 Model Building

3.4 The ARCH Model

3.5 The GARCH Model

3.6 The Integrated GARCH Model

3.7 The GARCH-M Model

3.8 The Exponential GARCH Model

3.9 The Threshold GARCH Model

3.10 The CHARMA Model

3.11 Random Coefficient Autoregressive Models

3.12 Stochastic Volatility Model

3.13 Long-Memory Stochastic Volatility Model

3.14 Application

3.15 Alternative Approaches

3.16 Kurtosis of GARCH Models

Appendix: Some RATS Programs for Estimating Volatility Models

Chapter 4: Nonlinear Models and Their Applications

4.1 Nonlinear Models

4.2 Nonlinearity Tests

4.3 Modeling

4.4 Forecasting

4.5 Application

Appendix A: Some RATS Programs for Nonlinear Volatility Models

Appendix B: R and S-Plus Commands for Neural Network

Chapter 5: High-Frequency Data Analysis and Market Microstructure

5.1 Nonsynchronous Trading

5.2 Bid–Ask Spread

5.3 Empirical Characteristics of Transactions Data

5.4 Models for Price Changes

5.5 Duration Models

5.6 Nonlinear Duration Models

5.7 Bivariate Models for Price Change and Duration

5.8 Application

Appendix A: Review of Some Probability Distributions

Appendix B: Hazard Function

Appendix C: Some RATS Programs for Duration Models

Chapter 6: Continuous-Time Models and Their Applications

6.1 Options

6.2 Some Continuous-Time Stochastic Processes

6.3 Ito's Lemma

6.4 Distributions of Stock Prices and Log Returns

6.5 Derivation of Black–Scholes Differential Equation

6.6 Black–Scholes Pricing Formulas

6.7 Extension of Ito's Lemma

6.8 Stochastic Integral

6.9 Jump Diffusion Models

6.10 Estimation of Continuous-Time Models

Appendix A: Integration of Black–Scholes Formula

Appendix B: Approximation to Standard Normal Probability

Chapter 7: Extreme Values, Quantiles, and Value at Risk

7.1 Value at Risk

7.2 RiskMetrics

7.3 Econometric Approach to VaR Calculation

7.4 Quantile Estimation

7.5 Extreme Value Theory

7.6 Extreme Value Approach to VaR

7.7 New Approach Based on the Extreme Value Theory

7.8 The Extremal Index

Chapter 8: Multivariate Time Series Analysis and Its Applications

8.1 Weak Stationarity and Cross-Correlation Matrices

8.2 Vector Autoregressive Models

8.3 Vector Moving-Average Models

8.4 Vector ARMA Models

8.5 Unit-Root Nonstationarity and Cointegration

8.6 Cointegrated VAR Models

8.7 Threshold Cointegration and Arbitrage

8.8 Pairs Trading

Appendix A: Review of Vectors and Matrices

Appendix B: Multivariate Normal Distributions

Appendix C: Some SCA Commands

Chapter 9: Principal Component Analysis and Factor Models

9.1 A Factor Model

9.2 Macroeconometric Factor Models

9.3 Fundamental Factor Models

9.4 Principal Component Analysis

9.5 Statistical Factor Analysis

9.6 Asymptotic Principal Component Analysis

Chapter 10: Multivariate Volatility Models and Their Applications

10.1 Exponentially Weighted Estimate

10.2 Some Multivariate GARCH Models

10.3 Reparameterization

10.4 GARCH Models for Bivariate Returns

10.5 Higher Dimensional Volatility Models

10.6 Factor–Volatility Models

10.7 Application

10.8 Multivariate t Distribution

10.9 Appendix: Some Remarks on Estimation

Chapter 11: State-Space Models and Kalman Filter

11.1 Local Trend Model

11.2 Linear State-Space Models

11.3 Model Transformation

11.4 Kalman Filter and Smoothing

11.5 Missing Values

11.6 Forecasting

11.7 Application

Chapter 12: Markov Chain Monte Carlo Methods with Applications

12.1 Markov Chain Simulation

12.2 Gibbs Sampling

12.3 Bayesian Inference

12.4 Alternative Algorithms

12.5 Linear Regression with Time Series Errors

12.6 Missing Values and Outliers

12.7 Stochastic Volatility Models

12.8 New Approach to SV Estimation

12.9 Markov Switching Models

12.10 Forecasting

12.11 Other Applications

Index

both

Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Tsay, Ruey S., 1951–

Analysis of financial time series / Ruey S. Tsay. – 3rd ed.

p. cm. – (Wiley series in probability and statistics)

Includes bibliographical references and index.

ISBN 978-0-470-41435-4 (cloth)

1. Time-series analysis. 2. Econometrics. 3. Risk management. I. Title.

HA30.3T76 2010

332.01′51955–dc22

2010005151

To Teresa and my father, and in memory of my mother

Preface

As many countries struggle to recover from the recent global financial crisis, one thing clear is that we do not want to suffer another crisis like this in the future. We must study the past in order to prevent future financial crisis. Financial data of the past few years thus become important in empirical study. The primary objective of the revision is to update the data used and to reanalyze the examples so that one can better understand the properties of asset returns. At the same time, we also witness many new developments in financial econometrics and financial software packages. In particular, the Rmetrics now has many packages for analyzing financial time series. The second goal of the revision is to include R commands and demonstrations, making it possible and easier for readers to reproduce the results shown in the book.

Collapses of big financial institutions during the crisis show that extreme events occur in clusters; they are not independent. To deal with dependence in extremes, I include the extremal index in Chapter 7 and discuss its impact on value at risk. I also rewrite Chapter 7 to make it easier to understand and more complete. It now contains the expected shortfall, or conditional value at risk, for measuring finanical risk.

Substantial efforts are made to draw a balance between the length and coverage of the book. I do not include credit risk or operational risk in this revision for three reasons. First, effective methods for assessing credit risk require further study. Second, the data are not widely available. Third, the length of the book is approaching my limit.

A brief summary of the added material in the third edition is:

1. To update the data used throughout the book.

2. To provide R commands and demonstrations. In some cases, R programs are given.

3. To reanalyze many examples with updated observations.

4. To introduce skew distributions for volatility modeling in Chapter 3.

5. To investigate properties of recent high-frequency trading data and to add applications of nonlinear duration models in Chapter 5.

6. To provide a unified approach to value at risk (VaR) via loss function, to discuss expected shortfall (ES), or equivalently the conditional value at risk (CVaR), and to introduce extremal index for dependence data in Chapter 7.

7. To discuss application of cointegration to pairs trading in Chapter 8.

8. To study applications of dynamic correlation models in Chapter 10.

I benefit greatly from constructive comments of many readers of the second edition, including students, colleagues, and friends. I am indebted to them all. In particular, I like to express my sincere thanks to Spencer Graves for creating the FinTS package for R and Tom Doan of ESTIMA and Eugene Gath for careful reading of the text. I also thank Kam Hamidieh for suggestions concerning new topics for the revision. I also like to thank colleagues at Wiley, especially Jackie Palmieri and Stephen Quigley, for their support. As always, the revision would not be possible without the constant encouragement and unconditional love of my wife and children. They are my motivation and source of energy. Part of my research is supported by the Booth School of Business, University of Chicago.

Finally, the website for the book is: http://faculty.chicagobooth.edu/ruey.tsay/teaching/fts3.

Ruey S. Tsay

Booth School of Business, University of Chicago

Chicago, Illinois

Preface to the Second Edition

The subject of financial time series analysis has attracted substantial attention in recent years, especially with the 2003 Nobel awards to Professors Robert Engle and Clive Granger. At the same time, the field of financial econometrics has undergone various new developments, especially in high-frequency finance, stochastic volatility, and software availability. There is a need to make the material more complete and accessible for advanced undergraduate and graduate students, practitioners, and researchers. The main goals in preparing this second edition have been to bring the book up to date both in new developments and empirical analysis, and to enlarge the core material of the book by including consistent covariance estimation under heteroscedasticity and serial correlation, alternative approaches to volatility modeling, financial factor models, state-space models, Kalman filtering, and estimation of stochastic diffusion models.

The book therefore has been extended to 12 chapters and substantially revised to include S-Plus commands and illustrations. Many empirical demonstrations and exercises are updated so that they include the most recent data.

The two new chapters are Chapter 9, Principal Component Analysis and Factor Models, and Chapter 11, State-Space Models and Kalman Filter. The factor models discussed include macroeconomic, fundamental, and statistical factor models. They are simple and powerful tools for analyzing high-dimensional financial data such as portfolio returns. Empirical examples are used to demonstrate the applications. The state-space model and Kalman filter are added to demonstrate their applicability in finance and ease in computation. They are used in Chapter 12 to estimate stochastic volatility models under the general Markov chain Monte Carlo (MCMC) framework. The estimation also uses the technique of forward filtering and backward sampling to gain computational efficiency.

A brief summary of the added material in the second edition is:

1. To update the data used throughout the book.

2. To provide S-Plus commands and demonstrations.

3. To consider unit-root tests and methods for consistent estimation of the covariance matrix in the presence of conditional heteroscedasticity and serial correlation in Chapter 2.

4. To describe alternative approaches to volatility modeling, including use of high-frequency transactions data and daily high and low prices of an asset in Chapter 3.

5. To give more applications of nonlinear models and methods in Chapter 4.

6. To introduce additional concepts and applications of value at risk in Chapter 7.

7. To discuss cointegrated vector AR models in Chapter 8.

8. To cover various multivariate volatility models in Chapter 10.

9. To add an effective MCMC method for estimating stochastic volatility models in Chapter 12.

The revision benefits greatly from constructive comments of colleagues, friends, and many readers of the first edition. I am indebted to them all. In particular, I thank J. C. Artigas, Spencer Graves, Chung-Ming Kuan, Henry Lin, Daniel Peña, Jeff Russell, Michael Steele, George Tiao, Mark Wohar, Eric Zivot, and students of my MBA classes on financial time series for their comments and discussions and Rosalyn Farkas for editorial assistance. I also thank my wife and children for their unconditional support and encouragements. Part of my research in financial econometrics is supported by the National Science Foundation, the High-Frequency Finance Project of the Institute of Economics, Academia Sinica, and the Graduate School of Business, University of Chicago.

Finally, the website for the book is: gsbwww.uchicago.edu/fac/ruey.tsay/teaching/fts2.

Ruey S. Tsay

University of Chicago

Chicago, Illinois

Preface to the First Edition

This book grew out of an MBA course in analysis of financial time series that I have been teaching at the University of Chicago since 1999. It also covers materials of Ph.D. courses in time series analysis that I taught over the years. It is an introductory book intended to provide a comprehensive and systematic account of financial econometric models and their application to modeling and prediction of financial time series data. The goals are to learn basic characteristics of financial data, understand the application of financial econometric models, and gain experience in analyzing financial time series.

The book will be useful as a text of time series analysis for MBA students with finance concentration or senior undergraduate and graduate students in business, economics, mathematics, and statistics who are interested in financial econometrics. The book is also a useful reference for researchers and practitioners in business, finance, and insurance facing value at risk calculation, volatility modeling, and analysis of serially correlated data.

The distinctive features of this book include the combination of recent developments in financial econometrics in the econometric and statistical literature. The developments discussed include the timely topics of value at risk (VaR), high-frequency data analysis, and Markov chain Monte Carlo (MCMC) methods. In particular, the book covers some recent results that are yet to appear in academic journals; see Chapter 6 on derivative pricing using jump diffusion with closed-form formulas, Chapter 7 on value at risk calculation using extreme value theory based on a nonhomogeneous two-dimensional Poisson process, and Chapter 9 on multivariate volatility models with time-varying correlations. MCMC methods are introduced because they are powerful and widely applicable in financial econometrics. These methods will be used extensively in the future.

Another distinctive feature of this book is the emphasis on real examples and data analysis. Real financial data are used throughout the book to demonstrate applications of the models and methods discussed. The analysis is carried out by using several computer packages; the SCA (the Scientific Computing Associates) for building linear time series models, the RATS (regression analysis for time series) for estimating volatility models, and the S-Plus for implementing neural networks and obtaining postscript plots. Some commands required to run these packages are given in appendixes of appropriate chapters. In particular, complicated RATS programs used to estimate multivariate volatility models are shown in Appendix A of Chapter 9. Some Fortran programs written by myself and others are used to price simple options, estimate extreme value models, calculate VaR, and carry out Bayesian analysis. Some data sets and programs are accessible from the World Wide Web at http://www.gsb.uchicago.edu/fac/ruey.tsay/teaching/fts.

The book begins with some basic characteristics of financial time series data in Chapter 1. The other chapters are divided into three parts. The first part, consisting of Chapters 2 to 7, focuses on analysis and application of univariate financial time series. The second part of the book covers Chapters 8 and 9 and is concerned with the return series of multiple assets. The final part of the book is Chapter 10, which introduces Bayesian inference in finance via MCMC methods.

A knowledge of basic statistical concepts is needed to fully understand the book. Throughout the chapters, I have provided a brief review of the necessary statistical concepts when they first appear. Even so, a prerequisite in statistics or business statistics that includes probability distributions and linear regression analysis is highly recommended. A knowledge of finance will be helpful in understanding the applications discussed throughout the book. However, readers with advanced background in econometrics and statistics can find interesting and challenging topics in many areas of the book.

An MBA course may consist of Chapters 2 and 3 as a core component, followed by some nonlinear methods (e.g., the neural network of Chapter 4 and the applications discussed in Chapters 5–7 and 10). Readers who are interested in Bayesian inference may start with the first five sections of Chapter 10.

Research in financial time series evolves rapidly and new results continue to appear regularly. Although I have attempted to provide broad coverage, there are many subjects that I do not cover or can only mention in passing.

I sincerely thank my teacher and dear friend, George C. Tiao, for his guidance, encouragement, and deep conviction regarding statistical applications over the years. I am grateful to Steve Quigley, Heather Haselkorn, Leslie Galen, Danielle LaCouriere, and Amy Hendrickson for making the publication of this book possible, to Richard Smith for sending me the estimation program of extreme value theory, to Bonnie K. Ray for helpful comments on several chapters, to Steve Kou for sending me his preprint on jump diffusion models, to Robert E. McCulloch for many years of collaboration on MCMC methods, to many students in my courses on analysis of financial time series for their feedback and inputs, and to Jeffrey Russell and Michael Zhang for insightful discussions concerning analysis of high-frequency financial data. To all these wonderful people I owe a deep sense of gratitude. I am also grateful for the support of the Graduate School of Business, University of Chicago and the National Science Foundation. Finally, my heartfelt thanks to my wife, Teresa, for her continuous support, encouragement, and understanding; to Julie, Richard, and Vicki for bringing me joy and inspirations; and to my parents for their love and care.

R. S. T.

Chicago, Illinois