Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters
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:||Jan 2010|
|Date of revision:|
|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.:
- Frank Smets, 2002.
"Output gap uncertainty: Does it matter for the Taylor rule?,"
Springer, vol. 27(1), pages 113-129.
- Frank Smets, 1998. "Output gap uncertainty: does it matter for the Taylor rule?," BIS Working Papers 60, Bank for International Settlements.
- Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Thomas J. Sargent & Mark W. Watson, 2007.
"ABCs (and Ds) of Understanding VARs,"
American Economic Review,
American Economic Association, vol. 97(3), pages 1021-1026, June.
- Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Thomas J. Sargent, 2005. "A,B,C's (and D's)'s for Understanding VARS," Levine's Bibliography 172782000000000096, UCLA Department of Economics.
- Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez & Thomas J. Sargent, 2005. "A, B, C’s (And D’s) For Understanding VARS," PIER Working Paper Archive 05-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Jesus Fernandez-Villaverde & Juan Rubio-Ramirez & Thomas J. Sargent, 2005. "A, B, C's (and D)'s for Understanding VARs," NBER Technical Working Papers 0308, National Bureau of Economic Research, Inc.
- Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Thomas J. Sargent & Mark Watson, 2006. "A,B,C's (and D's)'s for Understanding VARS," Levine's Bibliography 321307000000000646, UCLA Department of Economics.
- Jesús Fernández-Villaverde & Juan Francisco Rubio-Ramírez & Thomas J. Sargent, 2005. "A, B, C’s, (and D’s) for understanding VARs," FRB Atlanta Working Paper 2005-09, Federal Reserve Bank of Atlanta.
- Hamilton, James D., 1986. "A standard error for the estimated state vector of a state-space model," Journal of Econometrics, Elsevier, vol. 33(3), pages 387-397, December.
- Harvey, Andrew C. & Delle Monache, Davide, 2009. "Computing the mean square error of unobserved components extracted by misspecified time series models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 283-295, February.
- Tommaso Proietti & Alberto Musso & Thomas Westermann, 2007.
"Estimating potential output and the output gap for the euro area: a model-based production function approach,"
Springer, vol. 33(1), pages 85-113, July.
- Tommaso PROIETTI & Alberto MUSSO & Thomas WESTERMANN, 2002. "Estimating Potential Output and the Output Gap for the Euro Area: a Model-Based Production Function Approach," Economics Working Papers ECO2002/09, European University Institute.
- James H. Stock & Mark W. Watson, 2006.
"Why Has U.S. Inflation Become Harder to Forecast?,"
NBER Working Papers
12324, National Bureau of Economic Research, Inc.
- Ruiz, Esther & Rodríguez, Alejandro, 2008.
"Bootstrap prediction intervals in State Space models,"
DES - Working Papers. Statistics and Econometrics. WS
ws081104, Universidad Carlos III de Madrid. Departamento de Estadística.
- 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.
- Athanasios Orphanides & Simon Van_Norden, 2000.
"The Reliability of Output Gap Estimates in Real Time,"
Econometric Society World Congress 2000 Contributed Papers
0768, Econometric Society.
- Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
- Athanasios Orphanides & Simon van Norden, 2001. "The Unreliability of Output Gap Estimates in Real Time," CIRANO Working Papers 2001s-57, CIRANO.
- Athanasios Orphanides & Simon van Norden, 1999. "The Reliability of Output Gap Estimates in Real Time," Macroeconomics 9907006, EconWPA.
- Athanasios Orphanides & Simon van Norden, 1999. "The reliability of output gap estimates in real time," Finance and Economics Discussion Series 1999-38, Board of Governors of the Federal Reserve System (U.S.).
- J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
- James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
- Domenech, Rafael & Gomez, Victor, 2006. "Estimating Potential Output, Core Inflation, and the NAIRU as Latent Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 354-365, July.
- Ray, W. D., 1989. "Rates of convergence to steady state for the linear growth version of a dynamic linear model (DLM)," International Journal of Forecasting, Elsevier, vol. 5(4), pages 537-545.
- Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
- Douglas Staiger & James H. Stock & Mark W. Watson, 2001. "Prices, Wages and the U.S. NAIRU in the 1990s," NBER Working Papers 8320, National Bureau of Economic Research, Inc.
When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:ws100301. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ana Poveda)
If references are entirely missing, you can add them using this form.