Overview

The state-space approach provides a formal framework where any result or procedure developed for a basic model can be seamlessly applied to a standard formulation written in state-space form. Moreover, it can accommodate with a reasonable effort nonstandard situations, such as observation errors, aggregation constraints, or missing in-sample values. Exploring the advantages of this approach, State-Space Methods for Time Series Analysis: Theory, Applications and Software presents many computational procedures that can be applied to a previously specified linear model in state-space form. After discussing the formulation of the state-space model, the book illustrates the flexibility of the state-space representation and covers the main state estimation algorithms: filtering and smoothing. It then shows how to compute the Gaussian likelihood for unknown coefficients in the state-space matrices of a given model before introducing subspace methods and their application. It also discusses signal extraction, describes two algorithms to obtain the VARMAX matrices corresponding to any linear state-space model, and addresses several issues relating to the aggregation and disaggregation of time series. The book concludes with a cross-sectional extension to the classical state-space formulation in order to accommodate longitudinal or panel data. Missing data is a common occurrence here, and the book explains imputation procedures necessary to treat missingness in both exogenous and endogenous variables. Web Resource The authors’ E4 MATLAB® toolbox offers all the computational procedures, administrative and analytical functions, and related materials for time series analysis. This flexible, powerful, and free software tool enables readers to replicate the practical examples in the text and apply the procedures to their own work.

Full Product Details

Author:   Jose Casals (Universidad Complutense de Madrid, Spain) ,  Alfredo Garcia-Hiernaux (Universidad Complutense de Madrid, Spain) ,  Miguel Jerez ,  Sonia Sotoca (Universidad Complutense de Madrid, Spain)
Publisher:   Taylor & Francis Inc
Imprint:   Chapman & Hall/CRC
Dimensions:   Width: 15.60cm , Height: 2.30cm , Length: 23.40cm
Weight:   0.566kg
ISBN:  

9781482219593

ISBN 10:   148221959
Pages:   298
Publication Date:   23 March 2016
Audience:   College/higher education ,  Professional and scholarly ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Introduction Linear state-space models The multiple error model Single error models Model transformations Model decomposition Model combination Change of variables in the output Uses of these transformations Filtering and smoothing The conditional moments of a state-space model The Kalman filter Decomposition of the smoothed moments Smoothing for a general state-space model Smoothing for fixed-coefficients and single-error models Uncertainty of the smoothed estimates in a fixed-coefficients SEM Examples Likelihood computation for fixed-coefficients models Maximum likelihood estimation The likelihood for a non-stationary model The likelihood for a model with inputs Examples The likelihood of models with varying parameters Regression with time-varying parameters Periodic models The likelihood of models with GARCH errors Examples Subspace methods Theoretical foundations System order estimation Constrained estimation Multiplicative seasonal models Examples Signal extraction Input and error-related components Estimation of the deterministic components Decomposition of the stochastic component Structure of the method Examples The VARMAX representation of a state-space model Notation and previous results Obtaining the VARMAX form of a state-space model Practical applications and examples Aggregation and disaggregation of time series The effect of aggregation on a state-space model Observability in the aggregated model Specification of the high-frequency model Empirical example The cross-sectional extension: longitudinal and panel data Model formulation The Kalman filter The linear mixed model in state-space form Maximum likelihood estimation Missing data modifications Real data examples AppendicesAppendix A: Some results in numerical algebra and linear systems Appendix B: Asymptotic properties of maximum likelihood estimates Appendix C: Software (E4) Appendix D: Downloading E4 and the examples in this book Bibliography

Reviews

The way the authors of describe their book, it is the fruit of a long-lasting love affair with state space models, which started in the 1980s, inspired by the work of Box and Jenkins. Judging from the density of equations and symbols, it must be the theory of the subject that attracts them most. ... This book is not for the fainthearted. It explains a lotabout state space models. To use them, you have to accept the philosophy of detailed modelling of time series. In summary, if you are a specialist, or want to become one, you will like this book. - Paul Eilers, ISCB News, May 2017 This book synthesizes and presents the computational advantages of the state-space approach over the traditional time domain approaches to linear time series analysis. The explicit connection between the mainstream ARIMA time series models and the state-space representation, one of the main features of the book, is achieved by presenting many examples and procedures to combine, decompose, aggregate, and disaggregate an economic time series into the state-space form. More specifically, it provides a bridge for going back and forth between state-space models and the broad class of VARMAX models...Overall, this is a useful book on sate-space methods for time series analysis and covers substantial amount of material lucidly with a focus on computational aspects and software. It is an excellent reference book for self-study and can also be used as a companion for teaching time series analysis along with a standard time series text. -Mohsen Pourahmadi, Texas A&M University, in the Journal of Time Series Analysis, June 2017

The way the authors of describe their book, it is the fruit of a long-lasting love affair with state space models, which started in the 1980s, inspired by the work of Box and Jenkins. Judging from the density of equations and symbols, it must be the theory of the subject that attracts them most. ... This book is not for the fainthearted. It explains a lotabout state space models. To use them, you have to accept the philosophy of detailed modelling of time series. In summary, if you are a specialist, or want to become one, you will like this book. - Paul Eilers, ISCB News, May 2017 This book synthesizes and presents the computational advantages of the state-space approach over the traditional time domain approaches to linear time series analysis. The explicit connection between the mainstream ARIMA time series models and the state-space representation, one of the main features of the book, is achieved by presenting many examples and procedures to combine, decompose, aggregate, and disaggregate an economic time series into the state-space form. More specifically, it provides a bridge for going back and forth between state-space models and the broad class of VARMAX models...Overall, this is a useful book on sate-space methods for time series analysis and covers substantial amount of material lucidly with a focus on computational aspects and software. It is an excellent reference book for self-study and can also be used as a companion for teaching time series analysis along with a standard time series text. -Mohsen Pourahmadi, Texas A&M University, in the Journal of Time Series Analysis, June 2017

Author Information

Jose Casals is head of global risk management at Bankia. He is also an associate professor of econometrics at Universidad Complutense de Madrid. Alfredo Garcia-Hiernaux is an associate professor of econometrics at Universidad Complutense de Madrid and a freelance consultant. Miguel Jerez is an associate professor of econometrics at Universidad Complutense de Madrid and a freelance consultant. He was previously executive vice-president at Caja de Madrid for six years. Sonia Sotoca is an associate professor of econometrics at Universidad Complutense de Madrid. Drs. Casals, Garcia-Hiernaux, Jerez, and Sotoca are all engaged in a long-term research project to apply state-space techniques to standard econometric problems. Their common research interests include state-space methods and time series econometrics. A. Alexandre (Alex) Trindade is a professor of statistics in the Department of Mathematics and Statistics at Texas Tech University and an adjunct professor in the Graduate School of Biomedical Sciences at Texas Tech University Health Sciences Center. His research spans a broad swath of theoretical and computational statistics.

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