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Forecast evaluation of small nested model sets

  • Hubrich, Kirstin
  • West, Kenneth D.

We propose two new procedures for comparing the mean squared prediction error (MSPE) of a benchmark model to the MSPEs of a small set of alternative models that nest the benchmark. Our procedures compare the bench-mark to all the alternative models simultaneously rather than sequentially, and do not require re-estimation of models as part of a bootstrap procedure. Both procedures adjust MSPE differences in accordance with Clark and West (2007); one procedure then examines the maximum t-statistic, the other computes a chi-squared statistic. Our simulations examine the proposed procedures and two existing procedures that do not adjust the MSPE differences: a chi-squared statistic, and White’s (2000) reality check. In these simulations, the two statistics that adjust MSPE differences have most accurate size, and the procedure that looks at the maximum t-statistic has best power. We illustrate, our procedures by comparing forecasts of different models for U.S. inflation. JEL Classification: C32, C53, E37

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Paper provided by European Central Bank in its series Working Paper Series with number 1030.

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Date of creation: Mar 2009
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Handle: RePEc:ecb:ecbwps:20091030
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  1. West, Kenneth D. & Edison, Hali J. & Cho, Dongchul, 1993. "A utility-based comparison of some models of exchange rate volatility," Journal of International Economics, Elsevier, vol. 35(1-2), pages 23-45, August.
  2. Hubrich, Kirstin, 2005. "Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?," International Journal of Forecasting, Elsevier, vol. 21(1), pages 119-136.
  3. West, Kenneth D. & Cho, Dongchul, 1995. "The predictive ability of several models of exchange rate volatility," Journal of Econometrics, Elsevier, vol. 69(2), pages 367-391, October.
  4. Inoue, Atsushi & Kilian, Lutz, 2003. "On the selection of forecasting models," Working Paper Series 0214, European Central Bank.
  5. Todd E. Clark & Kenneth D. West, 2005. "Approximately normal tests for equal predictive accuracy in nested models," Research Working Paper RWP 05-05, Federal Reserve Bank of Kansas City.
  6. Orphanides, Athanasios & van Norden, Simon, 2005. "The Reliability of Inflation Forecasts Based on Output Gap Estimates in Real Time," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 583-601, June.
  7. 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.
  8. Todd E. Clark & Michael McCracken, 1999. "Tests of Equal Forecast Accuracy and Encompassing for Nested Models," Computing in Economics and Finance 1999 1241, Society for Computational Economics.
  9. Hendry, David F. & Hubrich, Kirstin, 2010. "Combining disaggregate forecasts or combining disaggregate information to forecast an aggregate," Working Paper Series 1155, European Central Bank.
  10. Inoue, Atsushi & Kilian, Lutz, 2002. "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?," CEPR Discussion Papers 3671, C.E.P.R. Discussion Papers.
  11. Sarno, Lucio & Daniel l Thornton & Giorgio Valente, 2003. "Federal Funds Rate Prediction," Royal Economic Society Annual Conference 2003 183, Royal Economic Society.
  12. Andrew Atkeson & Lee E. Ohanian., 2001. "Are Phillips curves useful for forecasting inflation?," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 2-11.
  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.
  14. Andreas Billmeier, 2004. "Ghostbusting; Which Output Gap Measure Really Matters?," IMF Working Papers 04/146, International Monetary Fund.
  15. Todd E. Clark & Kenneth D. West, 2004. "Using out-of-sample mean squared prediction errors to test the Martingale difference hypothesis," Research Working Paper RWP 04-03, Federal Reserve Bank of Kansas City.
  16. David Harvey & Paul Newbold, 2000. "Tests for multiple forecast encompassing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 471-482.
  17. Raffaella Giacomini & Halbert White, 2003. "Tests of Conditional Predictive Ability," Econometrics 0308001, EconWPA.
  18. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  19. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  20. West, K.D., 1994. "Asymptotic Inference About Predictive Ability," Working papers 9417, Wisconsin Madison - Social Systems.
  21. Yongmiao Hong & Tae-Hwy Lee, 2003. "Inference on Predictability of Foreign Exchange Rates via Generalized Spectrum and Nonlinear Time Series Models," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1048-1062, November.
  22. Lutkepohl, Helmut, 1984. "Forecasting Contemporaneously Aggregated Vector ARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 201-14, July.
  23. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
  24. Kirstin Hubrich & David F. Hendry, 2005. "Forecasting Aggregates by Disaggregates," Computing in Economics and Finance 2005 270, Society for Computational Economics.
  25. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  26. West, Kenneth D, 2001. "Tests for Forecast Encompassing When Forecasts Depend on Estimated Regression Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 29-33, January.
  27. Rapach, David E. & Wohar, Mark E., 2006. "In-sample vs. out-of-sample tests of stock return predictability in the context of data mining," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 231-247, March.
  28. Todd E. Clark & Michael W. McCracken, 2010. "Reality checks and nested forecast model comparisons," Working Papers 2010-032, Federal Reserve Bank of St. Louis.
  29. Ashley, R & Granger, C W J & Schmalensee, R, 1980. "Advertising and Aggregate Consumption: An Analysis of Causality," Econometrica, Econometric Society, vol. 48(5), pages 1149-67, July.
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