Wiley Foundations of Time Series Analysis and Prediction Theory: 379 (Wiley Series in Probability and Statistics)

From the Inside Flap Foundations of time series for researchers and students This 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. Product Description Foundations of time series for researchers and students This volume provides a mathematical foundation for time seriesanalysis and prediction theory using the idea of regression and thegeometry of Hilbert spaces. It presents an overview of the tools oftime series data analysis, a detailed structural analysis ofstationary processes through various reparameterizations employingtechniques from prediction theory, digital signal processing, andlinear algebra. The author emphasizes the foundation and structureof time series and backs up this coverage with theory andapplication. End-of-chapter exercises provide reinforcement for self-study andappendices covering multivariate distributions and Bayesianforecasting add useful reference material. Further coveragefeatures: * Similarities between time series analysis and longitudinal dataanalysis * Parsimonious modeling of covariance matrices through ARMA-likemodels * Fundamental roles of the Wold decomposition andorthogonalization * Applications in digital signal processing and Kalmanfiltering * Review of functional and harmonic analysis and predictiontheory Foundations of Time Series Analysis and Prediction Theory guidesreaders from the very applied principles of time series analysisthrough the most theoretical underpinnings of prediction theory. Itprovides a firm foundation for a widely applicable subject forstudents, researchers, and professionals in diverse scientificfields. Review "...provides a foundation for times series analysis and predictiontheory for researchers and advanced students..." (SciTech BookNews, Vol. 25, No. 4, December 2001) "...can be recommended as an excellent textbook (one of the bestwhich I have seen)." (Mathematical Reviews, 2002f) "...an excellent introduction to the remarkable developmentsduring the 20th century in the theory of time series analysis."(Journal of the American Statistical Association, December2002) From the Back Cover Foundations of time series for researchers and students This 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 back