Foundations of Time Series Analysis and Prediction Theory

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. Preface.

Acknowledgements.

Acronyms.

Introduction.

Time Series Analysis: One Long Series.

Time Series Analysis: Many Short Series.

Stationary ARMA Models.

Stationary Processes.

Parameterization and Prediction.

Finite Prediction and Partial Correlations.

Missing Values: Past and Future.

Stationary Sequences in Hilbert Spaces.

Stationarity and Hardy Spaces.

Appendix A: Multivariate Distributions.

Appendix B: The Bayesian Forecasting.

References.

Index.

Author Index. "...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) MOHSEN POURAHMADI, PhD, is Professor and Director of the Division of Statistics at Northern Illinois University in DeKalb, Illinois. 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 analysis
• Parsimonious modeling of covariance matrices through ARMA-like models
• Fundamental roles of the Wold decomposition and orthogonalization
• Applications in digital signal processing and Kalman filtering
• Review of functional and harmonic analysis and prediction theory

Foundations 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.