Mathematical Foundations of Time Series Analysis

This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.

Presents time series analysis in a reduced mathematical style Provides quick access to the essentials of time series analysis Serves as a reference work for students and researchers alike

Autorentext

Jan Beran is Professor of Statistics at the Department of Mathematics and Statistics at the University of Konstanz, Germany. After completing his Ph.D. in mathematics at the ETH Zurich, Switzerland, he worked at several universities in the USA and at the University of Zurich in Switzerland. He has a broad range of interests, from long-memory processes and asymptotic theory to applications in finance, biology, and musicology.

Inhalt
Introduction.- Typical assumptions.- Defining probability measure for time series.- Spectral representation of univariate time series.- Spectral representation of real valued vector time series.- Univariate ARMA processes.- Generalized autoregressive processes.- Prediction.- Inference for , and F.- Parametric estimation.- References.