Foundations of Time Series Analysis and Prediction Theory (Wiley Series in Probability and Statistics) Review

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(More customer reviews)This is an advanced text that covers the fundamentals of time series theory. It is split into three part with overlap to allow each part to be read independently. As Pourahmadi points out in his preface, the theory consists of time series modeling going back to the work of Schuster, Yule, Wold and others and the prediction theory developed by Wold, Kolmogorov, Cramer and others. The first part, chapters 1-4 covers most of the aspect of time series data analysis and is a mixture of theoretical and applied statistics. The rest of the book is very heavy on theroy and light on applications with part 2 covering chapters 5-8 which covers probability theory and the structure of stationary time series. This part is very theoretical but not extremely abstract. Part 3 is chapters 9 and 10 which are very abstract and cover the theory of Hilbert space, projections and Banach spaces (including a special function space defined on the open unit disc in the complex plane called a Hardy space). I am familiar with much of this abstract analysis from my graduate years in mathematics at the University of Maryland. But I have to confess that this having been 32 years ago, I don't remember much of it. Also I don't think I had ever heard of a Hardy space before.
The book is loaded with over 200 references going from the early 1930s to 2000.
If you have a graduate degree in mathematics or something comparable and are interested in the theory then I can recommend this book. But if you are just interested in learning the fundamentals of time series without abstract mathematics this book is not for you.

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Foundations of time series for researchers and studentsThis volume provides a mathematical foundation for time series analysis and prediction theory using the idea of regression and the geometry of Hilbert spaces. It presents an overview of the tools of time series data analysis, a detailed structural analysis of stationary processes through various reparameterizations employing techniques from prediction theory, digital signal processing, and linear algebra. The author emphasizes the foundation and structure of time series and backs up this coverage with theory and application.End-of-chapter exercises provide reinforcement for self-study and appendices covering multivariate distributions and Bayesian forecasting add useful reference material. Further coverage features:Similarities between time series analysis and longitudinal data analysisParsimonious modeling of covariance matrices through ARMA-like modelsFundamental roles of the Wold decomposition and orthogonalizationApplications in digital signal processing and Kalman filteringReview of functional and harmonic analysis and prediction theoryFoundations of Time Series Analysis and Prediction Theory guides readers from the very applied principles of time series analysis through the most theoretical underpinnings of prediction theory. It provides a firm foundation for a widely applicable subject for students, researchers, and professionals in diverse scientific fields.

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