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Forecast Evaluation of Small Nested Model Sets

  • Kirstin Hubrich
  • Kenneth D. West

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 benchmark to all the alternative models simultaneously rather than sequentially, and do not require reestimation 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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14601.

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Date of creation: Dec 2008
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Publication status: published as Kirstin Hubrich & Kenneth D. West, 2010. "Forecast evaluation of small nested model sets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 574-594.
Handle: RePEc:nbr:nberwo:14601
Note: AP ME TWP
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  1. 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.
  2. 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.
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  8. Todd E. Clark & Michael W. McCracken, 2000. "Tests of Equal Forecast Accuracy and Encompassing for Nested Models," Econometric Society World Congress 2000 Contributed Papers 0319, Econometric Society.
  9. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  10. Todd E. Clark & Michael W. McCracken, 2010. "Reality checks and nested forecast model comparisons," Working Papers 2010-032, Federal Reserve Bank of St. Louis.
  11. Lutkepohl, Helmut, 1984. "Forecasting Contemporaneously Aggregated Vector ARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 201-14, July.
  12. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
  13. 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.
  14. Giorgio Valente & Daniel Thornton & Lucio Sarno, 2004. "Federal Funds Rate Prediction," Working Papers wp04-12, Warwick Business School, Finance Group.
  15. Inoue, Atsushi & Kilian, Lutz, 2003. "On the selection of forecasting models," Working Paper Series 0214, European Central Bank.
  16. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
  17. David Harvey & Paul Newbold, 2000. "Tests for multiple forecast encompassing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 471-482.
  18. Kenneth D. West & Hali J. Edison & Dongchul Cho, 1993. "A utility based comparison of some models of exchange rate volatility," International Finance Discussion Papers 441, Board of Governors of the Federal Reserve System (U.S.).
  19. 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.
  20. 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.
  21. Hendry, David F. & Hubrich, Kirstin, 2010. "Combining disaggregate forecasts or combining disaggregate information to forecast an aggregate," Working Paper Series 1155, European Central Bank.
  22. 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.
  23. Hubrich, Kirstin, 2003. "Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?," Working Paper Series 0247, European Central Bank.
  24. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  25. 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.
  26. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  27. Andreas Billmeier, 2004. "Ghostbusting; Which Output Gap Measure Really Matters?," IMF Working Papers 04/146, International Monetary Fund.
  28. 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.
  29. Kirstin Hubrich & David F. Hendry, 2005. "Forecasting Aggregates by Disaggregates," Computing in Economics and Finance 2005 270, Society for Computational Economics.
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