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 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.
Author(s): Jacques J.F. Commandeur, Siem Jan Koopman
Series: Practical Econometrics
Publisher: Oxford University Press, USA
Year: 2007
Language: English
Commentary: 48544
Pages: 189
Tags: Финансово-экономические дисциплины;Эконометрика;
Contents......Page 8
List of Figures......Page 11
List of Tables......Page 15
1. Introduction......Page 16
2. The local level model......Page 24
2.1. Deterministic level......Page 25
2.2. Stochastic level......Page 30
2.3. The local level model and Norwegian fatalities......Page 33
3.1. Deterministic level and slope......Page 36
3.2. Stochastic level and slope......Page 38
3.3. Stochastic level and deterministic slope......Page 41
3.4. The local linear trend model and Finnish fatalities......Page 43
4. The local level model with seasonal......Page 47
4.1. Deterministic level and seasonal......Page 49
4.2. Stochastic level and seasonal......Page 53
4.3. Stochastic level and deterministic seasonal......Page 57
4.4. The local level and seasonal model and UK inflation......Page 58
5. The local level model with explanatory variable......Page 62
5.1. Deterministic level and explanatory variable......Page 63
5.2. Stochastic level and explanatory variable......Page 67
6. The local level model with intervention variable......Page 70
6.1. Deterministic level and intervention variable......Page 71
6.2. Stochastic level and intervention variable......Page 74
7. The UK seat belt and inflation models......Page 77
7.1. Deterministic level and seasonal......Page 78
7.2. Stochastic level and seasonal......Page 79
7.3. Stochastic level and deterministic seasonal......Page 82
7.4. The UK inflation model......Page 85
8.1. State space representation of univariate models......Page 88
8.2. Incorporating regression effects......Page 93
8.3. Confidence intervals......Page 96
8.4. Filtering and prediction......Page 99
8.5. Diagnostic tests......Page 105
8.6. Forecasting......Page 111
8.7. Missing observations......Page 118
9.1. State space representation of multivariate models......Page 122
9.2. Multivariate trend model with regression effects......Page 123
9.3. Common levels and slopes......Page 126
9.4. An illustration of multivariate state space analysis......Page 128
10.1.1. Stationary process......Page 137
10.1.2. Random process......Page 138
10.1.3. Moving average process......Page 140
10.1.4. Autoregressive process......Page 141
10.1.5. Autoregressive moving average process......Page 143
10.2. Non-stationary ARIMA models......Page 144
10.3. Unobserved components and ARIMA......Page 147
10.4. State space versus ARIMA approaches......Page 148
11.1. The STAMP program and SsfPack......Page 150
11.2. State space representation in SsfPack......Page 151
11.3. Incorporating regression and intervention effects......Page 154
11.4. Estimation of a model in SsfPack......Page 157
11.4.1. Likelihood evaluation using SsfLikEx......Page 159
11.4.2. The score vector......Page 161
11.4.3. Numerical maximisation of likelihood in Ox......Page 164
11.4.4. The EM algorithm......Page 165
11.4.5. Some illustrations in Ox......Page 166
11.5. Prediction, filtering, and smoothing......Page 169
12. Conclusions......Page 172
12.1. Further reading......Page 174
APPENDIX A. UK drivers KSI and petrol price......Page 177
APPENDIX B. Road traffic fatalities in Norway and Finland......Page 179
APPENDIX C. UK front and rear seat passengers KSI......Page 180
APPENDIX D. UK price changes......Page 182
Bibliography......Page 186
L......Page 188
W......Page 189
