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Non-linear and non-stationary time series analysis. Repr. of the 1988 ed. (English) Zbl 0687.62072

London etc.: Academic Press. viii, 237 p. £25.00 (1989).
The basic feature of time series analysis in the recent years was the departure from the assumptions of linearity and stationarity. The purpose of the book written by the famous researcher in this field is to bring together the main ideas concerning nonlinear and non-stationary models and to present them within a common unified framework.
In the part of the book treating the nonlinearity the bilinear, threshold autoregressive and exponential autoregressive models are studied together with the state dependent models including the latter as special cases. In the chapters concerning the non-stationary time series the emphasis is given to the idea of evolutionary spectrum.
The author of the well-known work “Spectral analysis and time series” (1981; Zbl 0537.62075), continues in his tradition of writing intelligible and interesting books. He prefers to explain the main ideas of the analysis for the presentation of complicated technical details. The theory is illustrated by many examples of the analysis of simulated time series as well as by real data sets, namely the celebrated Canadian lynx series and sunspot series. The book is very attractive for mathematicians and research workers who are specialized in the area of time series and their applications to physics, engineering and biology.
The contents of the book are the following. Chapter 1 presents a summary of the basic concepts of stationary processes and their spectral analysis. Chapter 2 gives a review of the classical theory of linear models. Chapter 3 deals with general forms of nonlinear models and introduces the topics of Volterra series expansions. polyspectra, and tests for nonlinearity. Chapter 4 describes some special classes of nonlinear models, with special emphasis on the treatment of bilinear, threshold autoregressive and exponential autoregressive models. Chapter 5 extends the discussion of nonlinear models to the general class of state- dependent models. Chapter 6 moves to the study of nonstationary processes and presents the theory of evolutionary spectra. Chapter 7 presents an extension of the classical Kolmogorov-Wiener theory of prediction and filtering to the case of nonstationary processes.
Reviewer: D.Jaruskova

MSC:

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