Time series: theory and methods. (English) Zbl 0604.62083

Brockwell, Peter J.; Davis, Richard A.

Springer Series in Statistics. New York etc.: Springer-Verlag. XIV, 519 p. DM 120.00 (1987).

This is a clearly written book intended to be a text for graduate students in statistics, mathematics, engineering and the natural or social sciences.
Chapter 1 introduces some basic ideas of stationarity, autocovariance function and techniques to estimate and remove trends and seasonality. Those aspects of Hilbert space theory, needed for a geometric understanding of the later chapters are studied in Chapter 2. Stationary ARMA processes are introduced in Chapter 3 and the spectral representation of stationary process is discussed in Chapter 4. The prediction problem, together with recursive methods for computing best linear predictors, is treated in Chapter 5 and some basic asymptotic theory in Chapter 6. Chapters 7 and 8 discuss estimation problems in time domain: the former develops estimates for the mean and autovariance function, while the latter considers the estimation of ARMA models.
Identification and forecasting for ARIMA models are dealt with in Chapter 9, while inferences for the spectrum of a stationary process is discussed in Chapter 10. Chapter 11 entertains some aspects of multivariate time series (basically the cross-spectrum and vector ARMA models) and the last chapter discusses some further topics: Kalman filtering, transfer function modelling and missing observations.
A further good aspect is the presence of exercises in the chapters. A companion diskette is available containing data sets and programs, written for the IBM PC.

Reviewer: P.A.Morettin

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62-02	Research exposition (monographs, survey articles) pertaining to statistics
62M15	Inference from stochastic processes and spectral analysis
62M20	Inference from stochastic processes and prediction
62M09	Non-Markovian processes: estimation

Keywords:

autocovariance function; Hilbert space theory; Stationary ARMA processes; spectral representation; prediction; best linear predictors; estimation problems in time domain; ARMA models; Identification; ARIMA models; multivariate time series; cross-spectrum; vector ARMA models; Kalman filtering; transfer function; missing observations