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Time Series Analysis: Forecasting and Control

George E. P. Box, Gwilym M. Jenkins, and Gregory C. Reinsel
John Wiley
Publication Date: 
Number of Pages: 
Wiley Series in Probability and Statistics
BLL Rating: 

The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Ita Cirovic Donev
, on

Time Series Analysis: Forecasting and Control is in its 4th edition. This classic text has set down roots in many student lives and many classrooms in graduate schools all over the world. Its style of presentation and clear discussion of relevant topics with an applied approach has been the main point of attraction. The book still lives a glamorous life and it will undoubtedly continue to do so in the future.

Naturally, the book starts out with a nice little introduction providing the appropriate motivation for the subject. The discussion is then divided into five parts: Stochastic Models and Their Forecasting, Stochastic Model Building, Transfer Function and Multivariable Model Building, Design of Discrete Control Schemes, and Charts and Tables. Let’s consider each section separately.

Part I concentrates on describing the structure of time series data and the models and forecasting methods that one can apply. First, the authors deal with stationary process continuing with the discussion of nonstationarity. Classical presentation of autocorrelation and stationarity is given along with some spectral properties. Mathematical exposition is followed by illustrative examples. The narrative style of discussion blends nicely with the more technical parts. Theoretical points are further explained with illustrations enabling the reader to easily visualize the problem at hand. Discussion of nonstationarity is continued in the same fashion. As a backbone example, the authors use stock prices, which are well known to follow a nonstationary process. There are not too many applied examples; instead, smaller (mostly theoretical) examples are presented. The chapter on forecasting is quite detailed. The process of model development is shown as a step-by-step method followed by a quite a number of examples.

Part II deals with building the stochastic model. It is divided into three main points: identification, estimation and diagnostics. The authors slowly introduce one to the problem at hand. The mathematics is clearly explained, and there is not much hand-waving. Chapters 9 and 10 give the reader an edge that usually is lacking in some competing books. They deal with seasonal models with and nonlinear and long-memory models. Much attention is devoted to these models. They are explained thoroughly, without skimping on the details. I especially liked the worked out examples. The authors use data sets given in Part V throughout the book. As the theory develops so does the understanding of the model presented. For example, in chapter 10 we come to the conclusion that the model we developed for an IBM stock is not adequate and hence needs a refinement using different method, i.e. IGARCH. This is particularly useful approach for students and practitioners without much of experience, as it gives a clear path for understanding why we use and apply different methods and why simple plug-and-play does not work in most cases.

In Part III we come to another important applied problem, that of estimating the transfer function. Discrete and continuous models are discussed along with model building, i.e., the identification, fitting and model checking. Again the theory is slowly built from previous chapters. The authors remind us where to take off from previous discussions. Examples take the form of the main discussion. They are presented in a very detailed manner, with illustrative calculations. Before moving on to multivariable analysis, outlier detection and intervention analysis are presented.

The last part of the book deals with the design of discrete control schemes. The narrative and detailed style of presentation is still much in effect. The main function of this last part is to bring together all the ideas presented. Thus, the authors refrain from the presentation of technicalities but rather stick to the narrative explanation and illustrations. The technical aspects are presented in detail in appendices.

One of the main positive aspects of the book is that the authors use the same data sets throughout the book (unlike some books where there are tons of examples but different for each chapter or topic of discussion), which enables the reader to really understand the data at hand and how they can be analyzed and modeled properly. It also provides the reader with the insight of where the models fail. This really gives another dimension to the book. Exercises are provided at the end of the book as a separate section. There are not a lot of exercises and problems, but enough to help students grasp the subject on the theoretical side. In my opinion there should be more applied problems or projects. References are plentiful and are provided in a standard manner at the end of the book. The index is quite detailed where one can actually find what one is looking for.

As for the negative aspects, I wished for more technical presentation inside the text rather than hidden in the appendices. This usually has a negative connotation to students, giving the impression that if one understands the method then it is somehow assumed that the technical aspects can be neglected and just moves on. (The fact that this attitude will likely let you down in the near future is of no concern.) In addition, I would like to see more and bigger problems that students could do as a semester project.

Overall, I think the book is very valuable and useful to graduate students in statistics, mathematics, engineering and the like. Also, it could be of tremendous help to practitioners. Even though the book is written in a clear, easy to follow narrative style with plenty of illustrations, one should nevertheless have a sufficient knowledge of graduate level mathematical statistics. By reading and understanding the book one should, in the end, feel very confident in time series analysis.

Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.



Preface to the Fourth Edition.

Preface to the Third Edition.

1. Introduction.

Part One: Stochastic Models and Their Forecasting. 

2. Autocorrelation Function and Spectrum of Stationary Processes.

3. Linear Stationary Models.

4. Linear Nonstationary Models.

5. Forecasting.

Part Two: Stochastic Model Building. 

6. Model Identification.

7. Model Estimation.

8. Model Diagnostic Checking.

9. Seasonal Models.

10. Nonlinear and Long Memory Models.

Part Three: Transfer Function and Multivariate Model Building. 

11. Transfer Function Models.

12. Identification, Fitting, and Checking of Transfer Function Models.

13. Intervention Analysis Models and Outlier detection.

14. Multivariate time Series Analysis.

Part Four: Design of Discrete Control Schemes. 

15. Aspects of Process Control.

Part Five: Charts and Tables. 

Collection of Tables and Charts.

Collection of Time Series Used for Examples in the Text and in Exercises.


Part Six: Exercises and Problems.