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.
Endofchapter exercises provide reinforcement for
selfstudy 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 ARMAlike 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.
