Bootstrap prediction intervals in State Space models

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dc.contributor.author Rodríguez, Alejandro
dc.contributor.author Ruiz Ortega, Esther
dc.contributor.editor Universidad Carlos III de Madrid. Departamento de Estadística
dc.date.accessioned 2008-03-06T09:09:24Z
dc.date.available 2008-03-06T09:09:24Z
dc.date.issued 2008-03
dc.identifier.uri http://hdl.handle.net/10016/1993
dc.description.abstract 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.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.language.iso eng
dc.relation.ispartofseries UC3M Working papers. Statistics and Econometrics
dc.relation.ispartofseries 08-04
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Backward representation
dc.subject.other Kalman filter
dc.subject.other Local Level Model
dc.subject.other Unobserved Components
dc.title Bootstrap prediction intervals in State Space models
dc.type workingPaper
dc.subject.eciencia Estadística
dc.rights.accessRights openAccess
dc.identifier.repec ws081104
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