Multivariate Time Series With Linear State Space Structure
This book presents a comprehensive study of multivariate time series with linear state space structure. The emphasis is put on both the clarity of the theoretical concepts and on efficient algorithms for implementing the theory. In particular, it in
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ultivariate Time Series With Linear State Space Structure
Multivariate Time Series With Linear State Space Structure
Víctor Gómez
Multivariate Time Series With Linear State Space Structure
123
Víctor Gómez Ministerio de Hacienda y Administraciones Públicas Dirección Gral. de Presupuestos Subdirección Gral. de Análisis y P.E. Madrid, Spain
ISBN 978-3-319-28598-6 DOI 10.1007/978-3-319-28599-3
ISBN 978-3-319-28599-3 (eBook)
Library of Congress Control Number: 2016938930 Mathematics Subject Classification (2010): 37M10, 62-XX, 62M10, 93E11, 62M20, 60Gxx, 65Fxx © Springer International Publishing Switzerland 2016 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
To my wife María C. and my daughter Berta
Preface
The subject of this book is the estimation of random vectors given observations of a related random process assuming that there is a linear relation between them. Since the class of linear models is very rich, we restrict our attention to those having a state space structure. The origin of this topic can be traced back to illustrious researches such as Laplace, Gauss, and Legendre and, more recently, to H. Wold, A.N. Kolmogorov, and N. Wiener in the late 1930s and earlier 1940s. The theory received a great impulse with the incorporation of state space models. The main contributor to this development was R.E. Kalman, who also made important related contributions to linear systems, optimal control, stability theory, etc. The subject matter of state space models has expanded a lot in recent years and today includes nonlinear as well as non-Gaussian models. We have limited the scope of the book to linear state space models, however, because otherwise its size would have been excessive. In this book, the emphasis is on the development of the theory of leastsquares estimation for finite-dimensional linear systems
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