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**The statistical analysis of time series.**
*(English)*
Zbl 0835.62074

Wiley Classics Library. Chichester: John Wiley & Sons Ltd. xiv, 704 p. (1994).

This is a widely known graduate-level textbook, published initially by Wiley in 1971, see the review Zbl 0225.62108, and that now is added to the Wiley Classics Library. It has a coverage of time series analysis, theory and methods, that proved useful for various kinds of time series analysis. The first chapters present methods that are justified on the basis of a simple model of a deterministic time function plus uncorrelated noise, so that standard least squares procedures are adequate. Then chapter 5 and 6 make the transition to stochastic models with a finite number of parameters and serial correlation, leading to the treatment of stationary stochastic processes in chapters 7, 8 and 9, in the time and frequency domain. A final chapter 10 deals with regression models with correlated error terms.

The point of view is that of “the mathematical theory of statistical inference concerning probabilistic models that are assumed to generate observed time series”. The book is carefully written, with a good collection of mostly theoretical exercises. By proper choice of the topics, courses at different levels of mathematical complexity can be based on the contents of the book.

When the book first appeared in 1971 there were still few systematic treatments of time series analysis. The area has grown considerably in the intervening 25 years, both in theory and in applications, and Anderson’s book has been one of the standard references for researchers in, and users of time series procedures.

The point of view is that of “the mathematical theory of statistical inference concerning probabilistic models that are assumed to generate observed time series”. The book is carefully written, with a good collection of mostly theoretical exercises. By proper choice of the topics, courses at different levels of mathematical complexity can be based on the contents of the book.

When the book first appeared in 1971 there were still few systematic treatments of time series analysis. The area has grown considerably in the intervening 25 years, both in theory and in applications, and Anderson’s book has been one of the standard references for researchers in, and users of time series procedures.

Reviewer: R.Mentz (S.M.de Tucuman)

### MSC:

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

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62M15 | Inference from stochastic processes and spectral analysis |

62M20 | Inference from stochastic processes and prediction |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

01A75 | Collected or selected works; reprintings or translations of classics |