Mathematical Foundations of Time Series Analysis A Concise Introduct
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 enablin
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Mathematical Foundations of Time Series Analysis A Concise Introduction
Mathematical Foundations of Time Series Analysis
Jan Beran
Mathematical Foundations of Time Series Analysis A Concise Introduction
123
Jan Beran Department of Mathematics and Statistics University of Konstanz Konstanz, Germany
ISBN 978-3-319-74378-3 ISBN 978-3-319-74380-6 (eBook) https://doi.org/10.1007/978-3-319-74380-6 Library of Congress Control Number: 2018930982 Mathematics Subject Classification (2010): 62Mxx, 62M10 © Springer International Publishing AG, part of Springer Nature 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
The historical development of time series analysis can be traced back to many applied sciences, including economics, meteorology, physics or communications engineering. Theoretical developments of the subject are closely linked to progress in the mathematical theory of stochastic processes and mathematical statistics. There are a number of excellent books on time series analysis, including Grenander and Rosenblatt (1957), Box and Jenkins (1970), Hannan (1970), Anderson (1971), Koopmans (1974), Fuller (1976), Priestley (1981), Brockwell and Davis (1991), Hamilton (1994), Diggle (1996), Brillinger (2001), Chatfield (2003), Lütkepohl (2006), Durbin and Koopmann (2012), Woodward et al. (2016), and Shumway and Stoffer (2017). Time series analysis is now a well-established scientific discipline with rigorous mathematical foundations. On the other hand, it is a very broad subject area, and, due to the diverse sciences that contributed to its development, the time series vocabulary is permeated with terminology reflecting t
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