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 inputsExamples 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 modelsExamples 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

"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