Applied Time Series Analysis With R

Time series data are data collected at regular intervals of time. Examples might include the daily high temperature at the airport in Manchester, NH, the annual number of deaths in New Hampshire due to drug overdoses, and the numbers generated by the decennial census. As the authors point out in their first paragraph, this means that time series data is fundamentally different from the data from which we make inferences in a first course in statistics. There we assume that each observation is independent of all the others. For time series data, this is rarely true. Typically, a value in a time series is highly correlated with the value of the immediately preceding and the immediately following observation. Today’s high temperature is much more likely to resemble yesterday’s or tomorrow’s than a randomly chosen day of the year. In addition, time series are usually not the result of random sampling or random assignment, Hence, their study is not just a generalization of what is studied in a first course to more groups or more variables. For that reason, a first course in time series can be a bit disorienting. On the other hand, time series data do make a natural example to mention in an introductory course of a common situation where the usual assumptions for inference are not met. And beware the introductory textbook that uses time series data to illustrate inference for regression!

The book at hand comes with little introduction. The authors mention using it in a course for Ph.D. students and also using it with masters students, but the name of the department, program, or course are not mentioned, nor are we told to what department the authors belong, nor in what discipline they obtained their degrees. Nor is there any mention of prerequisites. The latter, at least, can be filled in by examining the content of the book. Clearly an introductory statistics course is assumed as means and confidence intervals are discussed. Integrals and matrices scattered here and there suggest a solid background in mathemtics is required as well.

The presentation is more like a mathematics book than an applied statistics book. We see strings of definitions and a theorem or two preceding any examples. Initially, examples tend to be data simulated from a model under study rather than real data. Real examples do make appearances, usually at the ends of chapters, where they are helpful, but do not serve to motivate the exposition. Of course the same complaints could be made about many a mathematics textbook. And, indeed, this might be an excellent book for a mathematician wanting to learn more about the theory of time series. Unlike in most mathematics texts, however, the reader is often referred to the literature for proofs of the theorems stated. Exercises are a mix of computations and “show” type problems. Overall, the book seems to be above the level of most MBA programs.

Once past the initial challenge of trying to determine the level and intended audience, this book has much to recommend it for that audience. Coverage is quite thorough and up to date. There is an emphasis on the selection and evaluation of models which is very welcome, and not always found in statistics textbooks directed at non-statisticians.

The choice of the statistical programming language R may be controversial. While the tool of choice for many statisticians, R is not widely used elsewhere. It is, though, very powerful, free, and cross-platform. The first edition of this text relied on the Windows program WINKS, and in fact the book’s website is hosted by the WINKS people rather than the publisher. There you can find errata for the text and a link to what appears to be a free version of the commercial WINKS software. In their preface, the authors indicate that the switch to R was at the request of readers of the first edition, and indicate that they found WINKS much easier to use. Later in the book, though, they do admit that WINKS cannot do some of the most recent methods covered. R, on the other hand, is enhanced by the authors with a package one can download from wherever they downloaded R. It contains many extensions to R as well as many data sets. The text includes instruction on using this package, but seems to assume prior experience with R.

Turning to more mundane matters, the review copy arrived with the front cover one third detached from the pages, and another third heading in that direction. The binding appears to be more like that of a paperback than a traditional hardcover book. The “sustainably produced” pages look and feel a bit cheap, but in fact stand up to marginal notes and highlighting better than do most modern books. There is a fourteen page index and a ten page list of references.

After a few years in industry, Robert W. Hayden (bob@statland.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He contributed the chapter on evaluating introductory statistics textbooks to the MAA’s Teaching Statistics.