Mathematical foundations of time series analysis : a concise introduction /

Beran (Univ. of Konstanz, Germany) presents the mathematical foundations of time series analysis at a level suitable for advanced graduate students and researchers in statistics. The presentation is extremely concise, with essentially no motivating text or examples. Instead, the book gives definitions, theorems, and proofs, along with a few exercises and solutions. There is no discussion of software for time series analysis or applications. Readers will need to have extensive background in probability and mathematical statistics, real analysis, and functional analysis in order to follow the material. The book begins with basic definitions including stationarity and Gaussian processes. Four main chapters cover spectral representations and the properties of ARMA and GARCH processes. The book ends with three short chapters on parameter estimation, inference, and prediction. Because of its extremely concise format, this would not be appropriate for use as a textbook in an introductory course on time series analysis, but it may be useful to graduate students and researchers as a reference. Summing Up: Optional. Graduate students and above. --Brian Borchers, New Mexico Institute of Mining and Technology