Multivariate Time Series With Linear State Space Structure

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Springer, May 9, 2016 - Mathematics - 541 pages

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 investigates the relationship between VARMA and state space models, including canonical forms. It also highlights the relationship between Wiener-Kolmogorov and Kalman filtering both with an infinite and a finite sample. The strength of the book also lies in the numerous algorithms included for state space models that take advantage of the recursive nature of the models. Many of these algorithms can be made robust, fast, reliable and efficient. The book is accompanied by a MATLAB package called SSMMATLAB and a webpage presenting implemented algorithms with many examples and case studies. Though it lays a solid theoretical foundation, the book also focuses on practical application, and includes exercises in each chapter. It is intended for researchers and students working with linear state space models, and who are familiar with linear algebra and possess some knowledge of statistics.

 

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Contents

1 Orthogonal Projection
1
2 Linear Models
61
3 Stationarity and Linear Time Series Models
112
4 The State Space Model
213
5 Time Invariant State Space Models
323
6 Time Invariant State Space Models with Inputs
404
7 WienerKolmogorov Filtering and Smoothing
449
8 SSMMATLAB
520
Bibliography
527
Author Index
533
Subject Index
537
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About the author (2016)

Dr. Víctor Gómez is a statistician and technical advisor at the Spanish Ministry of Finance and Public Administrations in Madrid. His professional activity involves statistical, econometric and, above all, time series analysis of macroeconomic data, mostly in connection with short term economic analysis. More recently, he has focused on research in the field of time series analysis and the development of software for time series analysis. He has also taught numerous courses on time series analysis and related topics such as short-term forecasting, seasonal adjustment methods or time series filtering.

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