Jose Casals, Alfredo Garcia-Hiernaux, Miguel Jerez, Sonia Sotoca, A. Alexandre Trindade

State-Space Methods for Time Series Analysis (eBook, ePUB)

Theory, Applications and Software

• Format: ePub

Produktbeschreibung

Exploring the advantages of the state-space approach, this book presents numerous computational procedures that can be applied to a previously specified linear model in state-space form. It discusses model estimation and signal extraction; describes many procedures to combine, decompose, aggregate, and disaggregate a state-space form; and covers the connection between mainstream time series models and the state-space representation. Source code, a complete user manual, and other materials related to the authors' MATLAB® toolbox are available on a supplementary website.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 298
• Erscheinungstermin: 3. September 2018
• Englisch
• ISBN-13: 9781315360256
• Artikelnr.: 54781849

Autorenporträt

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.

Inhaltsangabe

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

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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

Appendices
Appendix 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

Rezensionen

"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