Bootstrap prediction intervals in State Space models
Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.
|Date of creation:||Mar 2008|
|Contact details of provider:|| Web page: http://portal.uc3m.es/portal/page/portal/dpto_estadistica|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ruiz, Esther & Broto, Carmen, 2006. "Using auxiliary residuals to detect conditional heteroscedasticity in inflation," DES - Working Papers. Statistics and Econometrics. WS ws060402, Universidad Carlos III de Madrid. Departamento de Estadística.
- Evans, Martin, 1991. "Discovering the Link between Inflation Rates and Inflation Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 169-184, May.
- Durbin, James & Koopman, Siem Jan, 2012.
"Time Series Analysis by State Space Methods,"
Oxford University Press,
edition 2, number 9780199641178.
- Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
- Tom Doan, "undated". "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- Laurence Ball & Stephen G. Cecchetti, 1990. "Inflation and Uncertainty at Long and Short Horizons," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 21(1), pages 215-254.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
- Cavaglia, Stefano, 1992. "The persistence of real interest differentials: A Kalman filtering approach," Journal of Monetary Economics, Elsevier, vol. 29(3), pages 429-443, June. Full references (including those not matched with items on IDEAS)