Parameter Space Restrictions in State Space Models
Article first published online: 17 JAN 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Journal of Forecasting
Volume 31, Issue 2, pages 109–123, March 2012
How to Cite
Jun, D. B., Kim, D. S., Park, S. and Park, M. H. (2012), Parameter Space Restrictions in State Space Models. J. Forecast., 31: 109–123. doi: 10.1002/for.1209
- Issue published online: 23 JAN 2012
- Article first published online: 17 JAN 2011
- state space models;
- ARIMA models;
- parameter space restrictions;
- trend–cycle decomposition
The state space model is widely used to handle time series data driven by related latent processes in many fields. In this article, we suggest a framework to examine the relationship between state space models and autoregressive integrated moving average (ARIMA) models by examining the existence and positive-definiteness conditions implied by auto-covariance structures. This study covers broad types of state space models frequently used in previous studies. We also suggest a simple statistical test to check whether a certain state space model is appropriate for the specific data. For illustration, we apply the suggested procedure in the analysis of the United States real gross domestic product data. Copyright © 2011 John Wiley & Sons, Ltd.