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Comparing forecast accuracy: A Monte Carlo investigation

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Author Info
Fabio Busetti () (Bank of Italy)
Juri Marcucci () (Bank of Italy)
Giovanni Veronese () (Bank of Italy)

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Abstract

The size and power properties of several tests of equal Mean Square Prediction Error (MSPE) and of Forecast Encompassing (FE) are evaluated, using Monte Carlo simulations, in the context of dynamic regressions. For nested models, the F-type test of forecast encompassing proposed by Clark and McCracken (2001) displays overall the best properties. However its power advantage tends to become smaller as the prediction sample increases and for multi-step ahead predictions; in these cases a standard FE test based on Gaussian critical values becomes relatively more attractive. The ranking among the tests remains broadly unaltered for one-step and multi-step ahead predictions, for partially misspecified models and for highly persistent data. A similar setup is then used to analyze the case of non-nested models. Again it is found that FE tests have a significantly better performance than tests of equal MSPE for discriminating between correct and misspecified models. An empirical application evaluates the predictive ability of nested and non-nested models for GDP in Italy and the euro-area.

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Publisher Info
Paper provided by Bank of Italy, Economic Research Department in its series Temi di discussione (Economic working papers) with number 723.

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Date of creation: Sep 2009
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Handle: RePEc:bdi:wptemi:td_723_09

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Related research
Keywords: Forecast encompassing; Model evaluation; Nested models; Non-nested models; Equal predictive ability;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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  1. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November. [Downloadable!] (restricted)
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  2. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
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  3. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October. [Downloadable!] (restricted)
  4. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May. [Downloadable!] (restricted)
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  5. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  6. West, Kenneth D., 2006. "Forecast Evaluation," Handbook of Economic Forecasting, Elsevier. [Downloadable!] (restricted)
  7. Chong, Yock Y & Hendry, David F, 1986. "Econometric Evaluation of Linear Macro-Economic Models," Review of Economic Studies, Blackwell Publishing, vol. 53(4), pages 671-90, August. [Downloadable!] (restricted)
  8. Giuseppe Parigi & Roberto Golinelli, 2007. "The use of monthly indicators to forecast quarterly GDP in the short run: an application to the G7 countries," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(2), pages 77-94. [Downloadable!]
  9. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November. [Downloadable!] (restricted)
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  10. Clark, Todd E. & West, Kenneth D., 2006. "Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 155-186. [Downloadable!] (restricted)
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  11. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September. [Downloadable!] (restricted)
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  12. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  13. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October. [Downloadable!] (restricted)
  14. Ericsson, Neil R., 1992. "Parameter constancy, mean square forecast errors, and measuring forecast performance: An exposition, extensions, and illustration," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 465-495, August. [Downloadable!] (restricted)
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  15. Todd E. Clark & Michael W. McCracken, 2009. "Improving Forecast Accuracy By Combining Recursive And Rolling Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 363-395, 05. [Downloadable!] (restricted)
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  16. Clark, Todd E. & McCracken, Michael W., 2005. "The power of tests of predictive ability in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 124(1), pages 1-31, January. [Downloadable!] (restricted)
  17. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
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