Time Series Analysis: Forecasting and Control – An interview with co-author Greta M. Ljung on the new edition of the bestseller

This month, Wiley is proud to publish the fifth edition of Time Series Analysis: Forecasting and Control. Bridging classical models and modern topics, the Fifth Edition of Time Series Analysis: Forecasting and Control maintains a balanced presentation of the tools for modeling and analyzing time series. Also describing the latest developments that have occurred in the field over the past decade through applications from areas such as business, finance, and engineering, the Fifth Edition continues to serve as one of the most influential and prominent works on the subject.

The new edition covers modern topics with new features that include:

  • A redesigned chapter on multivariate time series analysis with an expanded treatment of Vector Autoregressive, or VAR models, along with a discussion of the analytical tools needed for modeling vector time series
  • An expanded chapter on special topics covering unit root testing, time-varying volatility models such as ARCH and GARCH, nonlinear time series models, and long memory models
  • Numerous examples drawn from finance, economics, engineering, and other related fields
  • The use of the publicly available R software for graphical illustrations and numerical calculations along with scripts that demonstrate the use of R for model building and forecasting
  • Updates to literature references throughout and new end-of-chapter exercises
  • Streamlined chapter introductions and revisions that update and enhance the exposition

Time Series Analysis: Forecasting and Control, Fifth Edition is a valuable real-world reference for researchers and practitioners in time series analysis, econometrics, finance, and related fields. The book is also an excellent textbook for beginning graduate-level courses in advanced statistics, mathematics, economics, finance, engineering, and physics.


1. Congratulations on the fifth edition of the book, Time Series Analysis: Forecasting and Control which describes the use of stochastic models in five important areas of application: forecasting; determining the transfer function of a system; modeling the effects of intervention events; developing multivariate dynamic models; and designing simple control schemes. How did you join your co-authors? Have you worked together before?

Thank you so much. It is a great honor for me to join Professors Box, Jenkins, and Reinsel as co-author of this new edition. I was fortunate to have Professor Box as my Ph.D. advisor in the statistics graduate program at the University of Wisconsin-Madison. Our joint work at the time focussed on different aspects of time series analysis including parameter estimation and goodness-of-fit testing for ARIMA models, and analysis of variance with auto-correlated observations. Because of his vast experience, Professor Box had many research ideas and his goal was always to develop sound and practical solutions to important applied problems, rather than just theory for theory’s sake. It was a privilege to be able work with him and I was deeply honored when he invited me to work with him again on this new edition of his now classic book. Sadly, he did not see the project completed as he passed away in his home in Madison in March of 2013.

2. What were your main objectives during the writing process? What did you set out to achieve in reaching your readers?

Time series analysis has attracted considerable attention in recent years and many new developments have occurred in econometrics and other application areas. For example, the modeling of volatility in financial time series has continued to receive great attention in the literature, as has unit root testing, modeling of nonlinear time series, and modeling of vector time series. The purpose of preparing a new edition has been to update the book to reflect these developments. Some specific objectives have been to expand and reorganize some of the material, incorporate new literature, enhance the computational aspects of the book through the introduction of the R software, and increase the numbers of exercises in all chapters. For example, Chapter 14 on multivariate time series methods has been reorganized and expanded, placing more emphasis on Vector Autoregressive (VAR) models which are by far the most widely used vector models in applied work. Examples with illustrations in R are now part of the chapter and will help the users perform their own analysis. Chapter 10 on special topics has also been expanded and updated. This chapter now covers unit root testing, ARCH and GARCH models for analysis of volatility, modeling of nonlinear time series, and modeling of long-range dependence. Elsewhere in the book, other revisions have been made to enhance the exposition and bring the material up to date.

3. If there was one piece of information or advice that you would want your users to take away and remember after reading this, what would that be?

In the preface to the first edition of this book, Box and Jenkins stated that “Our objective will be to derive models possessing maximum simplicity and the minimum number of parameters consonant with representational adequacy.” They went on to show that many time series, including seasonal ones, can indeed be represented using models with relatively few parameters. Furthermore, once a suitable model has been found, optimal forecasts are readily computed from this model. It is interesting to note that this work was done during a period when large-scale macroeconomic forecasting models with hundreds, and often thousands, of equations were still being developed. The fact that bigger does not mean better has been confirmed by researchers comparing the forecasting performance of different models. A reason for why simple time series models can do well is that past values of a time series can serve as proxies for other variables not explicitly allowed for in the model.

4. Who should read the book and why?

As you noted above, the book provides a comprehensive account of a wide range of topics in time series analysis and forecasting. These include models and methods for analyzing univariate time series, transfer function-noise models for analyzing dynamic regression-type relationships between two or more time series, and multivariate time series methods that allow for full cross-sectional dependence between the series. The model building process is described in detail and illustrated using realistic examples drawn from business, economics, engineering, and other fields. Because of its broad coverage, the book is useful as a reference book for researchers and practitioners working in this field. The book is also useful as a textbook or as a supplementary text for advanced undergraduate and graduate level courses in time series analysis. An increase in the number of exercises in the current edition enhances its value as a textbook. In addition, the use of the R software for data analysis and graphical illustrations will be of value to anyone interested in analyzing real time series.

The class of time series models described in this book provide a flexible and convenient framework for analyzing and forecasting time series. These models are…as relevant today as they were when first introduced. In addition, the book covers numerous extensions and enhancements that have occurred in time series analysis… The advances in computing power and rapidly increasing use of the R software in time series analysis and other areas of statistics also make this new edition very timely.

5. Why is this edition of particular interest now?

The class of time series models described in this book provide a flexible and convenient framework for analyzing and forecasting time series. These models are widely used in applied work and are as relevant today as they were when first introduced. In addition, the book covers numerous extensions and enhancements that have occurred in time series analysis as a result of the wide-spread use of these models, bringing the material up-to-date and making the book current. The advances in computing power and rapidly increasing use of the R software in time series analysis and other areas of statistics also make this new edition very timely.

6. Were there areas of the book that you found more challenging to deal with, and if so, why?

Probably Chapter 14 on multivariate analysis. The material in this chapter was written at a rather theoretical level before and the goal here has been to simplify the presentation and make it more accessible to the readers. Another priority was to keep the book down to a reasonable size. The previous edition was over 700 pages long and our goal was to slightly shorten this new edition. With new material to be added, this meant that some earlier material had to be condensed or removed, but without altering the original character of the book.

7. What is it about this particular area that fascinates you?

In a time series, successive observations are typically correlated and this leads to some unique challenges that are not present in many other areas of statistics. For example, standard statistical procedures such as the ordinary t and F tests are typically not valid in the presence of serial correlation. The intervention analysis methods described in Chapter 13 of this book provide a way to overcome such problems. These methods use an ARIMA model to describe the serial correlation and add an indicator variable to account for level shifts and other external effects, resulting in a transfer function-noise model for the final series. Similar approaches can be used to deal with outliers and missing values in time series. The ARIMA class of models have a flexible correlation structure and have been remarkably successful for a wide range of applications. Research to deal with features not well accounted for by these models, such as nonlinearities and long-range dependence sometimes seen in hydrological time series and time-varying volatility common in financial time series, have been under development for some time and continue to receive attention among researchers. Multivariate time series analysis is another interesting area. This area is more challenging but new and useful tools continue to be developed as described, for example, in a 2014 Wiley book by Ruey Tsay.    


8. What will be your next book-length undertaking?

There are some potential projects that I am pursuing but it is still too early to share any details. But, just between us, I am hoping that this will not be my last collaboration with Wiley.

9. Please could you tell us more about your educational background and what was it that brought you to recognise statistics as a discipline in the first place?

I received my undergraduate degree in psychology from Åbo Academy in Finland. I was very interested in psychometrics, and in topics such as test construction, factor analysis, and experimental design, which all involved a fair amount of statistics. I took several courses in statistics and towards the end of the program I decided to continue my studies in this area. After graduating, I spent eight months at the University of Uppsala studying statistics under the direction of Professor Herman Wold, who was interested in econometrics and had made some important early contributions to time series analysis. I also started to consider graduate programs in the United States, inspired by a friend who was going to Stanford University as a Fulbright scholar. I applied to three universities in the U.S. and ended up going to the University of Wisconsin-Madison, which turned out to be a good choice for me.

10.  George Box sadly passed away in early 2013. Please could you talk about his work with Gwilym Jenkins?

The collaboration between them started in the early 1960s and led to the publication of the first edition of this book in 1970, followed by a second edition in 1976. The original focus of their work was to develop optimal control schemes for an industrial process where a variable under one’s control could be manipulated so as to minimize disturbances in the process output. As they worked on this problem, they realized the need to forecast future deviations of the output from target values, and this led them to look for time series models that could be used for forecasting. An early paper on the control problem, published in JRSS B in 1962, was referred to as a “landmark paper”, and was included in Volume II of Breakthroughs in Statistics published by Springer in 1993. Nevertheless, the book that followed had only its last chapter devoted to the control problem, while the rest of the book dealt with time series modeling and forecasting.

The publication of the book received immediate attention and has had a big impact on the theory and practice of time series analysis. This is evidenced by subsequent developments in the field, along with direct statements of individuals who have contributed to these developments. For example, Clive Granger, who along with Robert Engle was awarded the Nobel Prize in Economic Sciences in 2003, listed the opportunity to preview a copy of the first edition of Box and Jenkins book as one of the ten lucky breaks in his professional life as it pointed him to a research area that turned out to be very productive. Earlier in 1986, when Granger wrote the introduction to the time series part of The Collected Works of George E.P. Box, Volume II, he described the contributions of Box and Jenkins and concluded by saying “The Box-Jenkins modeling strategy and the models proposed are standard in many disciplines, but particularly in econometrics. Forecasts based on these methods, which are data-analysis intensive, are usually very hard to beat by alternative methods, even when time-varying parameters, nonlinearities, or structural constraints are introduced. What makes his work most remarkable is that it represents only one of George Box’s several interests”. These other interests included response surface methods, design of experiments, Bayesian methods, robustness, quality, and process control, all areas where he made strong contributions.

Readers interested in more details about the work of George Box and his collaboration with Gwilym Jenkins are also encouraged to read a 2001 interview with Professor Box conducted by Daniel Pena in the International Journal of Forecasting, as well as George Box’s own recollections in An Accidental Statistician published by Wiley in 2013. George Box was a friend to his students and he is greatly missed.