AbstractAbstract: Prediction under model uncertainty is an important and difficult issue. Traditional prediction methods (such as pretesting) are based on model selection followed by prediction in the selected model, but the reported prediction and the reported prediction variance ignore the uncertainty from the selection procedure. This paper proposes a weighted average least squares (WALS) prediction procedure that is not conditional on the selected model. Taking both model and error uncertainty into account, we also propose an appropriate estimate of the variance of the WALS predictor. Correlations among the random errors are explicitly allowed. Compared to other prediction averaging methods, the WALS predictor has important advantages both theoretically and computationally. Simulation studies show that the WALS predictor generally produces lower mean squared prediction errors than its competitors, and that the proposed estimator for the prediction variance performs particularly well when model uncertainty increases.
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 Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-043.
Date of creation: 2012
Date of revision:
Contact details of provider:
Web page: http://center.uvt.nl
Model averaging; Model uncertainty; Bayesian analysis; Prediction;
This paper has been announced in the following NEP Reports:
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.:
- Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
- Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
- Hilde C. Bjørnland & Karsten R. Gerdrup & Anne Sofie Jore & Leif Anders Thorsrud & Christie Smith, 2010.
"Does forecast combination improve Norges Bank inflation forecasts?,"
0002, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
- Hilde C. Bjørnland & Karsten Gerdrup & Anne Sofie Jore & Christie Smith & Leif Anders Thorsrud, 2012. "Does Forecast Combination Improve Norges Bank Inflation Forecasts?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(2), pages 163-179, 04.
- Hilde C. Bjørnland & Karsten Gerdrup & Anne Sofie Jore & Christie Smith & Leif Anders Thorsrud, 2009. "Does forecast combination improve Norges Bank inflation forecasts?," Working Paper 2009/01, Norges Bank.
- Jan R. Magnus, 2002. "Estimation of the mean of a univariate normal distribution with known variance," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 225-236, June.
- Giles, Judith A & Giles, David E A, 1993. " Pre-test Estimation and Testing in Econometrics: Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 7(2), pages 145-97, June.
- Aiolfi, Marco & Timmermann, Allan, 2006. "Persistence in forecasting performance and conditional combination strategies," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 31-53.
- Wan, Alan T. K. & Zou, Guohua, 2003. "Optimal critical values of pre-tests when estimating the regression error variance: analytical findings under a general loss structure," Journal of Econometrics, Elsevier, vol. 114(1), pages 165-196, May.
- Jacobson, Tor & Karlsson, Sune, 2002.
"Finding Good Predictors for Inflation: A Bayesian Model Averaging Approach,"
Working Paper Series
138, Sveriges Riksbank (Central Bank of Sweden).
- Sune Karlsson & Tor Jacobson, 2004. "Finding good predictors for inflation: a Bayesian model averaging approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(7), pages 479-496.
- Jan R. Magnus & Dmitry Danilov, 2004.
"Forecast accuracy after pretesting with an application to the stock market,"
Journal of Forecasting,
John Wiley & Sons, Ltd., vol. 23(4), pages 251-274.
- Danilov, D.L. & Magnus, J.R., 2002. "Forecast Accuracy after Pretesting with an Application to the Stock Market," Discussion Paper 2002-76, Tilburg University, Center for Economic Research.
- Ohtani, Kazuhiro & Toyoda, Toshihisa, 1980. "Estimation of regression coefficients after a preliminary test for homoscedasticity," Journal of Econometrics, Elsevier, vol. 12(2), pages 151-159, February.
- Toyoda, Toshihsa & Wallace, T D, 1976. "Optimal Critical Values for Pre-Testing in Regression," Econometrica, Econometric Society, vol. 44(2), pages 365-75, March.
- Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
- Elliott, Graham & Timmermann, Allan, 2004.
"Optimal forecast combinations under general loss functions and forecast error distributions,"
Journal of Econometrics,
Elsevier, vol. 122(1), pages 47-79, September.
- Elliott, Graham & Timmermann, Allan, 2002. "Optimal Forecast Combination Under General Loss Functions and Forecast Error Distributions," University of California at San Diego, Economics Working Paper Series qt15r9t2q2, Department of Economics, UC San Diego.
- Yang, Yuhong, 2004. "Combining Forecasting Procedures: Some Theoretical Results," Econometric Theory, Cambridge University Press, vol. 20(01), pages 176-222, February.
- Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
- Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).
If references are entirely missing, you can add them using this form.