*(English)*Zbl 0858.62072

This is a new edition [for the review of the 2nd, 1976-edition see Zbl 0363.62069] of a widely used book on the statistics of time series. It is divided into four substantive parts, as follows: Part 1, Stochastic Models and their Forecasting, is an introduction to linear stationary models with finite numbers of parameters, in particular ARMA (mixed autoregressive-moving average) processes, their probabilistic and forecasting properties. It is a feature of the book that time-domain considerations prevail, against frequency-domain arguments. Part 2, Stochastic Model Building, covers the basic statistical approach. Here, non-stationary series are considered, but such that suitable differencing reduces them to stationarity: these are the ARIMA (I for integrated) models. Empirical analysis is done by intensively using a given data set (time series), in cycles of identification, estimation and checking. The final chapter in this part applies these elements to seasonal models. Part 3 extends the approach to Transfer Function Models; their probabilistic structure is described, previous to empirical fitting. An interesting new chapter in this part is devoted to intervention analysis and outlier detection. Part 4 is on Design of Discrete Control Schemes. The final portion of the book collects tables, charts, data sets, exercises and problems, references and a detailed index.

In relation to the original edition, there are modifications in the chapter on estimation, and additions such as canonical correlation analysis, use of model selection criteria, testing for unit roots, nonstationarity in ARIMA processes, state representation of ARMA models, score tests, structural components, and others.

The first edition of this book appeared in 1970, see the review Zbl 0249.62009, at a time when comparatively few book on time series were available. It proposed a practical approach to the empirical analysis, that was adopted by many statisticians and workers in a wide diversity of fields. In the intervening 25 years, the field of statistical time series grew enormously: many books and monographs were published, new journals were created, and the number of specialists and users of the methods grew accordingly. It is easy to predict that this new edition will hold a key place in the time series area. The book has been considerably updated, retaining the initial level and approach.

Gwilym M. Jenkins, co-author of the first edition, died several years ago, and the present edition, that incorporates G. C. Reinsel as co-author, is dedicated to his memory.

##### MSC:

62M10 | Time series, auto-correlation, regression, etc. (statistics) |

62-01 | Textbooks (statistics) |

62M20 | Prediction; filtering (statistics) |