RT Generic
T1 Bootstrap prediction intervals in State Space models
A1 Rodríguez, Alejandro
A1 Ruiz Ortega, Esther
A2 Universidad Carlos III de Madrid. Departamento de Estadística, 
AB Prediction intervals in State Space models can be obtained by assuming Gaussian innovations andusing the prediction equations of the Kalman filter, where the true parameters are substituted byconsistent estimates. This approach has two limitations. First, it does not incorporate theuncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovationsmay be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtainprediction intervals by using a bootstrap procedure that requires the backward representation ofthe model. Obtaining this representation increases the complexity of the procedure and limits itsimplementation to models for which it exists. The bootstrap procedure proposed by Wall andStoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errorsinstead of for the observations. In this paper, we propose a bootstrap procedure for constructingprediction intervals in State Space models that does not need the backward representation of themodel and is based on obtaining the intervals directly for the observations. Therefore, itsapplication 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 Walland Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results byimplementing the new procedure to obtain prediction intervals for future values of a real timeseries.
YR 2008
FD 2008-03
LK https://hdl.handle.net/10016/1993
UL https://hdl.handle.net/10016/1993
LA eng
LA eng
DS e-Archivo
RD 27 jul. 2024