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Time series analysis and its applications. (English) Zbl 0942.62098

Springer Texts in Statistics. New York, NY: Springer. xiii, 549 p. (2000).
The book describes statistical methods used in time series analysis in the time domain as well as in the frequency domain. Theoretical results are illustrated on simulated and real data, which include Johnson & Johnson quarterly earnings, global warming, speech data, El Niño and fish populations, functional magnetic resonance imaging, and earthquakes and explosions. All data sets are posted on the www at the authors’ URLs and also an exploratory data analysis program can be downloaded as freeware from these websites.
The book starts with characteristics of time series such as autocorrelation and cross correlation functions and their estimates. Then ARMA, ARIMA, long memory, threshold, and ARCH models are described. The frequency domain approach contains power spectrum and cross spectrum, linear filters, periodogram, nonparametric and parametric spectral estimation, lagged regression models, signal extraction, optimum filtering, and spectral analysis of multidimensional series. A special chapter is devoted to state-space and multivariate ARMAX models. The authors describe filtering, smoothing, forecasting, ML estimation, structural models, bootstrapping, dynamic linear models with switching, stochastic volatility, and other topics. The last chapter contains statistical methods in the frequency domain. Here the authors deal with regression for jointly stationary series, regression with deterministic inputs, random coefficient regression, analysis of designed experiments, discriminant and cluster analysis, principal components, canonical and factor analysis, the spectral envelope, and wavelets problems.
Although the methods described in the book are quite complicated, the authors present them very clearly and in an understandable way. Numerical examples help to understand how the models can be applied in statistical analysis of real data. The book can be recommended as a very useful textbook for students as well as a reference book for researchers.
Reviewer: J.Anděl (Praha)

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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
62Pxx Applications of statistics

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