An Introduction to State Space Time Series Analysis

by Jacques J.F. Commandeur, Siem Jan Koopman

Overview

Providing a practical introduction to state space methods as applied to unobserved components time series models, also known as structural time series models, this book introduces time series analysis using state space methodology to readers who are neither familiar with time series analysis, nor with state space methods. The only background required in order to understand the material presented in the book is a basic knowledge of classical linear regression models, of which a brief review is provided to refresh the reader's knowledge. Also, a few sections assume familiarity with matrix algebra, however, these sections may be skipped without losing the flow of the exposition. The book offers a step by step approach to the analysis of the salient features in time series such as the trend, seasonal, and irregular components. Practical problems such as forecasting and missing values are treated in some detail. This useful book will appeal to practitioners and researchers who use time series on a daily basis in areas such as the social sciences, quantitative history, biology and medicine. It also serves as an accompanying textbook for a basic time series course in econometrics and statistics, typically at an advanced undergraduate level or graduate level.

Product Details

ISBN-13:	9780191607806
Publisher:	OUP Oxford
Publication date:	07/19/2007
Series:	Practical Econometrics
Sold by:	Barnes & Noble
Format:	eBook
File size:	12 MB
Note:	This product may take a few minutes to download.

About the Author

Jacques J.F. Commandeur is Senior Researcher at the SWOV Institute for Road Safety Research, Leidschendam, The Netherlands. His Ph.D. is from the Department of Psychometrics and Research Methodology of Leiden University. Between 1991 and 2000 he did research for the Department of Data Theory and the Department of Educational Sciences at Leiden University in the fields of multidimensional scaling and nonlinear multivariate data analysis. Since 2000 he has been at SWOV researching the statistical and methodological aspects of road safety research in general, and time series analysis of developments in road safety in particular. His research interests are Procrustes analysis; Multidimensional scaling; Distance-based multivariate analysis; Statistical analysis of time series; Forecasting. He has published in international journals in psychometrics and chemometrics. Siem Jan Koopman is Professor of Econometrics at the Free University Amsterdam and the Tinbergen Institute. His Ph.D. is from the London School of Economics (LSE) and he has held positions at the LSE between 1992 and 1997 and at the CentER (Tilburg University) between 1997 and 1999. In 2002 he visited the US Bureau of the Census in Washington DC as an ASA / NSF / US Census / BLS Research Fellow. His research interests are Statistical analysis of time series; Theoretical and applied time series econometrics; Financial econometrics; Simulation methods; Kalman filtering and smoothing; Forecasting. He has published in many international journals in statistics and econometrics.

Table of Contents

List of Figures x

List of Tables xiv

1 Introduction 1

2 The local level model 9

2.1 Deterministic level 10

2.2 Stochastic level 15

2.3 The local level model and Norwegian fatalities 18

3 The local linear trend model 21

3.1 Deterministic level and slope 21

3.2 Stochastic level and slope 23

3.3 Stochastic level and deterministic slope 26

3.4 The local linear trend model and Finnish fatalities 28

4 The local level model with seasonal 32

4.1 Deterministic level and seasonal 34

4.2 Stochastic level and seasonal 38

4.3 Stochastic level and deterministic seasonal 42

4.4 The local level and seasonal model and UK inflation 43

5 The local level model with explanatory variable 47

5.1 Deterministic level and explanatory variable 48

5.2 Stochastic level and explanatory variable 52

6 The local level model with intervention variable 55

6.1 Deterministic level and intervention variable 56

6.2 Stochastic level and intervention variable 59

7 The UK seat belt and inflation models 62

7.1 Deterministic level and seasonal 63

7.2 Stochastic level and seasonal 64

7.3 Stochastic level and deterministic seasonal 67

7.4 The UK inflation model 70

8 General treatment of univariate state space models 73

8.1 State space representation of univariate models 73

8.2 Incorporating regression effects 78

8.3 Confidence intervals 81

8.4 Filtering and prediction 84

8.5 Diagnostic tests 90

8.6 Forecasting 96

8.7 Missing observations 103

9 Multivariate time series analysis 107

9.1 State space representation of multivariate models 107

9.2 Multivariate trend model with regression effects 108

9.3 Common levels and slopes 111

9.4 An illustration ofmultivariate state space analysis 113

10 State space and Box-Jenkins methods for time series analysis 122

10.1 Stationary processes and related concepts 122

10.1.1 Stationary process 122

10.1.2 Random process 123

10.1.3 Moving average process 125

10.1.4 Autoregressive process 126

10.1.5 Autoregressive moving average process 128

10.2 Non-stationary ARIMA models 129

10.3 Unobserved components and ARIMA 132

10.4 State space versus ARIMA approaches 133

11 State space modelling in practice 135

11.1 The STAMP program and Ssfpack 135

11.2 State space representation in SsfPack 136

11.3 Incorporating regression and intervention effects 139

11.4 Estimation of a model in SsfPack 142

11.4.1 Likelihood evaluation using SsfLikEx 144

11.4.2 The score vector 146

11.4.3 Numerical maximisation of likelihood in Ox 149

11.4.4 The EM algorithm 150

11.4.5 Some illustrations in Ox 151

11.5 Prediction, filtering, and smoothing 154

12 Conclusions 157

12.1 Further reading 159

Appendix A UK drivers KSI and petrol price 162

Appendix B Road traffic fatalities in Norway and Finland 164

Appendix C UK front and rear seat passengers KSI 165

Appendix D UK price changes 167

Bibliography 171

Index 173