Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters
In the context of linear state space models with known parameters, the Kalman filter (KF) generates best linear unbiased predictions of the underlying states together with their corresponding Prediction Mean Square Errors (PMSE). However, in practice, when the filter is run with the parameters substituted by consistent estimates, the corresponding PMSE do not take into account the parameter uncertainty. Consequently, they underestimate their true counterparts. In this paper, we propose two new bootstrap procedures to obtain PMSE of the unobserved states designed to incorporate this latter uncertainty. We show that the new bootstrap procedures have better finite sample properties than bootstrap alternatives and than procedures based on the asymptotic approximation of the parameter distribution. The proposed procedures are implemented for estimating the PMSE of several key unobservable US macroeconomic variables as the output gap, the Non-accelerating Inflation Rate of Unemployment (NAIRU), the long-run investment rate and the core inflation. We show that taking into account the parameter uncertainty may change their prediction intervals and, consequently, the conclusions about the utility of the NAIRU as a macroeconomic indicator for expansions and recessions.
If 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- 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.
- Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Thomas J. Sargent, 2005.
"A,B,C's (and D's)'s for Understanding VARS,"
172782000000000096, UCLA Department of Economics.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Athanasios Orphanides & Simon van Norden, 1999.
"The Reliability of Output Gap Estimates in Real Time,"
- 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, 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, 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.).
- Athanasios Orphanides & Simon van Norden, 2001. "The Unreliability of Output Gap Estimates in Real Time," CIRANO Working Papers 2001s-57, CIRANO.
- 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.
- 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.
- 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.
- Frank Smets, 1998.
"Output gap uncertainty: does it matter for the Taylor rule?,"
BIS Working Papers
60, Bank for International Settlements.
- Frank Smets, 2002. "Output gap uncertainty: Does it matter for the Taylor rule?," Empirical Economics, Springer, vol. 27(1), pages 113-129.
- 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.
- 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.
- 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.
- 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.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:1:p:62-74. 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: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.