State-Space Methods for Time Series Analysis

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.

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