Multivariate Time Series With Linear State Space Structure

1. Front Matter

   Pages i-xvii

   PDF

2. Orthogonal Projection

   • Víctor Gómez

   Pages 1-60

3. Linear Models

   • Víctor Gómez

   Pages 61-111

4. Stationarity and Linear Time Series Models

   • Víctor Gómez

   Pages 113-211

5. The State Space Model

   • Víctor Gómez

   Pages 213-322

6. Time Invariant State Space Models

   • Víctor Gómez

   Pages 323-403

7. Time Invariant State Space Models with Inputs

   • Víctor Gómez

   Pages 405-447

8. Wiener–Kolmogorov Filtering and Smoothing

   • Víctor Gómez

   Pages 449-519

9. SSMMATLAB

   • Víctor Gómez

   Pages 521-526

10. Back Matter

    Pages 527-541

    PDF

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 intendedfor researchers and students working with linear state space models, and who are familiar with linear algebra and possess some knowledge of statistics.

• 37M10, 62-XX, 62M10, 93E11, 62M20, 60Gxx, 65Fxx
• time series
• state space models
• signal extraction
• Kalman filter
• forecasting
• smoothing
• multivariate time series
• algorithms for state space models
• MATLAB
• Wiener-Kolmogorov theory

“The book under review is a mathematically solid and comprehensive text, covering in detail the main ingredients of linear estimation theory in state space models. Its emphasis is on the state estimation problems, rather than on statistical inference of the unknown parameters of the model, and from this point of view its scope and spirit is closer to the engineering literature, and to the standard reference … .” (Pavel Chigansky, Mathematical Reviews, May, 2017)

• Dirección Gral. de Presupuestos,Subdirec, Ministerio de Hacienda y Administracione, Madrid, Spain

  Víctor Gómez

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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