Time series. A biostatistical introduction.

*(English)*Zbl 0727.62083
Oxford Science Publications; Oxford Statistical Science Series, 5. Oxford: Clarendon Press. xi, 257 p. £35.00/hbk; £15.00/pbk (1990).

The book reacts on the fact that most introductory books on time-series analysis take their principal motivation either from economics (emphasizing various forecasting methods) or from signal processing (mainly in engineering). This book covers this subject from the point of view of applications in biology, integrating analyses of biological data (listed in the appendix) into the methodological development. It is also reasonable that some emphasis is put on analysis of short, replicated series which are common in biological applications.

The book assumes that the reader has a knowledge of basic probability theory, statistical methods, matrix algebra and calculus. The matrix approach to the general linear model and the manipulation of complex numbers are outlined in the appendix. The contents of the book are the following:

1. Introduction: basic concepts, including trend, serial dependence and stationarity; 2. Simple descriptive methods of analysis: time plots, smoothing, differencing, estimating the autocorrelation function, periodogram; 3. Theory of stationary processes: theoretical material on stationary random processes (spectrum, linear filters, ARMA, sampling and accumulation); 4. Spectral analysis: periodogram-based tests of white noise, FFT, estimates of spectrum, fitting parametric models; 5. Repeated measurements; 6. Fitting autoregressive moving average processes to data; 7. Forecasting; 8. Elements of bivariate time-series analysis: cross- correlation function, estimating the cross-spectrum.

The book assumes that the reader has a knowledge of basic probability theory, statistical methods, matrix algebra and calculus. The matrix approach to the general linear model and the manipulation of complex numbers are outlined in the appendix. The contents of the book are the following:

1. Introduction: basic concepts, including trend, serial dependence and stationarity; 2. Simple descriptive methods of analysis: time plots, smoothing, differencing, estimating the autocorrelation function, periodogram; 3. Theory of stationary processes: theoretical material on stationary random processes (spectrum, linear filters, ARMA, sampling and accumulation); 4. Spectral analysis: periodogram-based tests of white noise, FFT, estimates of spectrum, fitting parametric models; 5. Repeated measurements; 6. Fitting autoregressive moving average processes to data; 7. Forecasting; 8. Elements of bivariate time-series analysis: cross- correlation function, estimating the cross-spectrum.

Reviewer: T.Cipra (Praha)

##### MSC:

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

62M15 | Inference from stochastic processes and spectral analysis |

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

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62M20 | Inference from stochastic processes and prediction |