##
**Time series analysis.**
*(English)*
Zbl 0831.62061

Princeton, NJ: Princeton University Press. xiv, 799 p. (1994).

The book consists of 22 chapters and 4 appendices. Each chapter is finished with its own appendix to which more complicated proofs are relegated. Most of the chapters contain also some exercises. The following topics are included:

1. Difference equations; 2. Lag operators; 3. Stationary ARMA processes; 4. Forecasting; 5. Maximum likelihood estimation; 6. Spectral analysis; 7. Asymptotic distribution theory; 8. Linear regression models; 9. Linear systems of simultaneous equations; 10. Covariance-stationary vector processes; 11. Vector autoregressions; 12. Bayesian analysis; 13. The Kalman filter; 14. Generalized method of moments; 15. Models of nonstationary time series; 16. Processes with deterministic time trends; 17. Univariate processes with unit roots; 18. Unit roots in multivariate time series; 19. Cointegration; 20. Full-information maximum likelihood analysis of cointegrated systems; 21. Time series models of heteroskedasticity; 22. Modeling time series with changes in regime.

The appendices are: A. Mathematical review (trigonometry, complex numbers, calculus, matrix algebra, probability and statistics); B. Statistical tables; C. Answers to selected exercises; D. Greek letters and mathematical symbols used in the text.

The author wrote the book as a textbook for a graduate econometric course in time series analysis. All necessary mathematical tools are briefly, rigorously, and very carefully introduced. Attention is paid also to numerical methods which are needed to solve the problems. The presentation of the text is really lucid so that classical results as well as modern developments are made accessible also to nonspecialists. The numerous examples illustrate how the theoretical results can be used in applications, mainly in modern macroeconometrics and finance.

The book covers many topics from the modern time series analysis, especially those which the author considers as important in econometrics. On the other hand, the book is not intended to be an encyclopaedia, and so, for example, criteria for determining the order of a model, threshold models, and nonlinear models are not mentioned.

The reviewer very appreciates this book as a textbook and recommends it for courses in time series analysis. The care which the author devoted to the organization of the material, and to the choice of methods and examples, saves a lot of time and work for teachers as well as for students.

1. Difference equations; 2. Lag operators; 3. Stationary ARMA processes; 4. Forecasting; 5. Maximum likelihood estimation; 6. Spectral analysis; 7. Asymptotic distribution theory; 8. Linear regression models; 9. Linear systems of simultaneous equations; 10. Covariance-stationary vector processes; 11. Vector autoregressions; 12. Bayesian analysis; 13. The Kalman filter; 14. Generalized method of moments; 15. Models of nonstationary time series; 16. Processes with deterministic time trends; 17. Univariate processes with unit roots; 18. Unit roots in multivariate time series; 19. Cointegration; 20. Full-information maximum likelihood analysis of cointegrated systems; 21. Time series models of heteroskedasticity; 22. Modeling time series with changes in regime.

The appendices are: A. Mathematical review (trigonometry, complex numbers, calculus, matrix algebra, probability and statistics); B. Statistical tables; C. Answers to selected exercises; D. Greek letters and mathematical symbols used in the text.

The author wrote the book as a textbook for a graduate econometric course in time series analysis. All necessary mathematical tools are briefly, rigorously, and very carefully introduced. Attention is paid also to numerical methods which are needed to solve the problems. The presentation of the text is really lucid so that classical results as well as modern developments are made accessible also to nonspecialists. The numerous examples illustrate how the theoretical results can be used in applications, mainly in modern macroeconometrics and finance.

The book covers many topics from the modern time series analysis, especially those which the author considers as important in econometrics. On the other hand, the book is not intended to be an encyclopaedia, and so, for example, criteria for determining the order of a model, threshold models, and nonlinear models are not mentioned.

The reviewer very appreciates this book as a textbook and recommends it for courses in time series analysis. The care which the author devoted to the organization of the material, and to the choice of methods and examples, saves a lot of time and work for teachers as well as for students.

Reviewer: J.Anděl (Praha)

### MSC:

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

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

62P20 | Applications of statistics to economics |

62M15 | Inference from stochastic processes and spectral analysis |