Foundations of time series Analysis and prediction theory

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; and 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.

Contents

• Preface
• Acknowledgements
• Introduction
• Time Series Analysis: One Long Series
• Time Series Analysis: Many Short Series
• Stationary ARMA Models
• Stationary Process
• Parameterization and Prediction
• Finite Prediction and Partial Correlations
• Past and Future: Missing Values
• Stationary Sequences in Hilbert Spaces
• Stationarity and Hardy Spaces
• Appendix A: Multivariate Distributions
• Appendix B: The Bayesian Forecasting
• References
• Index