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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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:
Contact details of provider:
Postal: C/ Madrid, 126 - 28903 GETAFE (MADRID)
Web page: http://www.uc3m.es/uc3m/dpto/DEE/departamento.html
More information through EDIRC
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.:
- Durbin, James & Koopman, Siem Jan, 2001.
"Time Series Analysis by State Space Methods,"
Oxford University Press, number 9780198523543, September.
- Tom Doan, . "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- 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.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994.
"Multivariate Stochastic Variance Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Tom Doan, . "RATS programs to estimate multivariate stochastic volatility models," Statistical Software Components RTZ00093, 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.
- Carmen Broto & Esther Ruiz, 2006. "Using Auxiliary Residuals To Detect Conditional Heteroscedasticity In Inflation," Statistics and Econometrics Working Papers ws060402, Universidad Carlos III, Departamento de Estadística y Econometría.
- Evans, Martin, 1991. "Discovering the Link between Inflation Rates and Inflation Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 169-84, May.
- Rodríguez, Alejandro & Ruiz, Esther, 2012.
"Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters,"
Computational Statistics & Data Analysis,
Elsevier, vol. 56(1), pages 62-74, January.
- Alejandro Rodríguez & Esther Ruiz, 2010. "Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters," Statistics and Econometrics Working Papers ws100301, Universidad Carlos III, Departamento de Estadística y Econometría.
- Ng, Jason & Forbes, Catherine S. & Martin, Gael M. & McCabe, Brendan P.M., 2013.
"Non-parametric estimation of forecast distributions in non-Gaussian, non-linear state space models,"
International Journal of Forecasting,
Elsevier, vol. 29(3), pages 411-430.
- Jason Ng & Catherine S. Forbes & Gael M. Martin & Brendan P.M. McCabe, 2011. "Non-Parametric Estimation of Forecast Distributions in Non-Gaussian, Non-linear State Space Models," Monash Econometrics and Business Statistics Working Papers 11/11, Monash University, Department of Econometrics and Business Statistics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.