Practical Time Series

what these methods may potentially accomplish and what risks they entail. Brief summaries explain the related theory in plain prose. Numerous references direct the interested reader to more information on speciŽ c details and tangents, theoretical results, and special applications. In addition, the data for four real world applications can be found on the author’s website (http://www.bath.ac.uk/ mascc/). This book covers such a broad range of topics in time series and forecasting that it is difŽ cult to summarize its contents in a meaningful way. Thus I have listed the main topics of each chapter and highlighted especially useful and interesting discussions by the author on particular topics. Chapter 1 gives an overview of the book’s scope. It addresses the crucial differences between “method” and “model” and between univariate and multivariate methods. It also discusses the problems of judgment forecasts, the importance of formulating a problem carefully, and the dangers of extrapolation inherent in forecasting. Chapter 2 reviews the basic terminology of time series analysis. The many topics covered include measurement scales, objectives of time series analyses, seasonal variation and trend, basic graphical methods and transformations of data, stochastic process theory, autocorrelation and autocovariance, the classiŽ cation of univariate models [e.g., random walks, autoregressive (AR) models, moving averages (MA)], and correlograms. Chapter 3 covers an extensive range of univariate models. It begins with autoregressive integrated moving average (ARIMA) models (and their parts), and the related issues of seasonality, periodicity, fractional models, and unit roots. It continues with state-space models, growth curve models, nonlinear models (e.g., ARCH and GARCH models), and provides a thoughtfully skeptical discussion of the “hot topics” of neural nets (NNs) and chaos. Section 3.5 focuses on model building, selection, and checking and includes a helpful list of guiding concepts (p. 80). Chapter 4 focuses on univariate forecasting methods, the heart of the book. It Ž rst describes the general problem of prediction and loss functions, then compares and contrasts model-based forecasting methods [e.g., Box–Jenkins (ARIMA) procedure, Kalman Ž lters, nonlinear models] and ad hoc forecasting methods (e.g., Holt–Winters procedure, combinations of forecasts). Chapter 5 covers multivariate forecasting methods and discusses why they are so much harder than univariate methods. The concepts covered here include feedback, openand closed-loop systems, the problem of out-ofsample forecasts, leading indicators, and multivariate cross-correlations. It then presents a strong argument that regression models are generally inappropriate for time series problems and uses this discussion to motivate the development of alternative models (p. 117). These alternatives include transfer function models, vector versions of ARIMA models, error-correction models (based on cointegration), and econometric models, among others. Chapters 6–8 shift from a consideration of models and methods to the goals of forecasting. These chapters would be well worth reading for experts in the aforementioned methods to gain from the author’s broad perspective. Chapter 6 gives a comparative assessment of forecasting methods, starting with a list of practical criteria for choosing the “best” forecast. It also considers measures of forecast accuracy (e.g., PMSE, MAE, MAPE) and discusses lessons learned from forecasting competitions and case studies. Finally, it gives advice on strategies for choosing a forecasting model, including several helpful lists of criteria (pp. 170, 173, and 178). Next, Chapter 7 discusses the challenges of interval forecasting. It extensively reviews methods for constructing prediction intervals (e.g., model, approximate, empirical, simulation, and Bayesian-based methods). It then compares the results of different methods, explains why prediction intervals tend to be too narrow in practice, and concludes with some practical recommendations for constructing prediction intervals (p. 213). Chapter 8 discusses the many sources of model uncertainty and their impact on forecast accuracy. It also examines the balance between model building and data dredging, and illustrates this with an example of NN models applied to Box–Jenkins’ classical airline data. It ends with cautionary advice about model selection and a discussion of practical methods for dealing with model uncertainty. Finally, the book contains an extensive list of references, with notes as to where each reference is cited. One of the book’s strengths is that after presenting a topic, the author routinely brings his personal views and experiences into the picture. Another strength is the numerous checklists of ideas throughout, which serve to clarify concepts and reinforce key points that are easy to forget. The author’s advice comes across as thoughtful guidance, and makes this book more interesting to read. Nonetheless, I wish that this book had included a few more real-world applications and that it had developed those that are presented more fully. To some extent, the limited number of such examples and the briefness of detail re ect the nature of reference books. Nevertheless, given the author’s clear sense of the need to analyze problems in terms of their applied context, I think that the foregoing suggestion would have enhanced the presentation of his perspective, especially in the Ž nal chapters. In summary, this book represents a helpful and enlightening reference for practicing statisticians (among others) who work with time series and forecasting applications and who wish to think critically about current practice in these areas. This book could also be the core text of a graduate seminar on forecasting for students with a good background in time series analysis. Hopefully, some bright and ambitious students will be stimulated to tackle the diverse open questions and statistical challenges that the author raises.