If there is a book on time series that I would recommend then it would be Tsay's Analysis of Financial Time Series. Yes, the concentration is on financial time series, but one can easily learn time series analysis from this book. The 2nd edition makes this learning experience even easier and more fun with the addition of the S-Plus code. Such additions are always the most welcomed by students. It is really hard to characterize this book because it looks like a reference book, but it really isn't; on the other hand, it can serve as a time series analysis text, but in principle it isn't that either. However, one thing is certain: for financial practitioners and students interested in mathematical finance this book will be a little gem and will stand proud on their shelves.
This is no big theory book on time series. Theoretical concepts are presented but not in a theorem-proof style. The author supports his theoretical developments by presenting many examples and the accompanying S-Plus code as well as the output. Each chapter ends with a set of exercises and a bibliography. Most of the exercises are computational and applied, which again confirms that this is a book that one will learn to "understand" time series analysis. For readers who wish a very theoretical approach to time series analysis should consult other text like Time Series: Theory and Methods by Brockwell and Davis or Time Series Analysis by Hamilton. On the other hand for those not interested in the very theoretical aspects of the time series analysis, I would recommend taking this book on rather than something like Schumway and Stoffer's Time Series Analysis and its Applications. Tsay's book will provide much more insight.
The new edition not only brings updated exercises and S-Plus code, but also addition of new chapters. So what's the book about? Chapter 1 is an introductory chapter where basic distributional properties of returns are given. This is followed by the coverage of linear time series models. Moving average, ARIMA, seasonality and unit-roots tests are presented. Chapter 3 deals with the concept of heteroscedasticity. Nonlinear models and high frequency analysis are treated next. Continuous time models give a general description that can be found in almost any mathematical finance text. The heart of the chapter is the Black-Scholes model along with jump diffusion models. Chapter 7 essentially deals with Value at Risk. Tsay presents the theoretical concepts explaining the extreme value theory and quantile estimation. However, the concepts of VaR require much more (at least for a practitioner). Tsay gives a good theoretical background where the reader can extend this to the practical and even more theoretical aspects, by reading Holton's Value at Risk: Theory and Practice. Chapter 10 considers multivariate volatility models. It is a good continuation of chapter 3 where the univariate volatility models were discussed. The last part of the book deals with Kalman filter and the Markov Chain Monte Carlo methods.
All in all this is an excellent account on financial time series and I would recommend it to students and especially to practitioners, who really need a book with enough of theoretical concepts to base the explanations but also with plenty of intuitive insight of how exactly these models work and how one can apply them in practice. Students should appreciate a book like this as it will give them the necessary "how to" and "why" answers.
Ita Cirovic Donev is a PhD candidate at the University of Zagreb. She hold a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical mehods of credit and market risk. Apart from the academic work she does consulting work for financial institutions.