Bootstrap prediction intervals in State Space models
AbstractPrediction 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.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws081104.
Date of creation: Mar 2008
Date of revision:
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Backward representation; Kalman filter; Local Level Model; Unobserved Components;
Other versions of this item:
- Alejandro Rodriguez & Esther Ruiz, 2009. "Bootstrap prediction intervals in state-space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 167-178, 03.
- NEP-ALL-2008-04-04 (All new papers)
- NEP-ECM-2008-04-04 (Econometrics)
- NEP-ETS-2008-04-04 (Econometric Time Series)
- NEP-FOR-2008-04-04 (Forecasting)
- NEP-ORE-2008-04-04 (Operations Research)
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.:
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