Mathematical Foundations of Time Series Analysis: A Concise Introduction

by Jan Beran

Overview

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.

Product Details

ISBN-13:	9783030089757
Publisher:	Springer International Publishing
Publication date:	12/11/2018
Edition description:	Softcover reprint of the original 1st ed. 2017
Pages:	307
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of Contents

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 μ, γ and F.- Parametric estimation.- References.

Editorial Reviews

‘This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. … 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.’ … The book can be recommended to all readers, who are interested in this field.” (Ludwig Paditz, zbMath 1414.62001, 2019)

“This book is a rigorous, mathematically clear and self-contained and quite complete text on time series analysis, suitable both for graduate courses and as a reference book for researchers and users of shastic temporal models.” (Nazaré Mendes Lopes, Mathematical Reviews, December, 2018)

“Beran (Univ. of Konstanz, Germany) presents the mathematical foundations of time series analysis at a level suitable for advanced graduate students and researchers in statistics. The presentation is extremely concise … . the book gives definitions, theorems, and proofs, along with a few exercises and solutions. … it may be useful to graduate students and researchers as a reference.” (B. Borchers, Choice, Vol. 56 (03), November, 2018)​

From the Publisher