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Forecast evaluation of small nested model sets

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Author Info
Kirstin Hubrich () (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.)
Kenneth D. West () (University of Wisconsin, Madison, Department of Economics, 1180 Observatory Drive, Madison, WI 53706, USA.)

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Abstract

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. JEL Classification: C32, C53, E37.

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

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Length: 46 pages
Date of creation: Mar 2009
Date of revision:
Handle: RePEc:ecb:ecbwps:20091030

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Related research
Keywords: Out-of-sample; prediction; testing; multiple model comparisons; inflation forecasting.;

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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. 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)
  3. 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. [Downloadable!] (restricted)
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  4. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  5. 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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  6. 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. [Downloadable!] (restricted)
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  7. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, 02. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
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  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. Lutkepohl, Helmut, 1984. "Forecasting Contemporaneously Aggregated Vector ARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 201-14, July.
  11. David Harvey & Paul Newbold, 2000. "Tests for multiple forecast encompassing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 471-482. [Downloadable!]
  12. 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.
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  13. 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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  14. 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. [Downloadable!]
  15. 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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  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. [Downloadable!] (restricted)
  17. Sarno, Lucio & Thornton, Daniel L & Valente, Giorgio, 2005. "Federal Funds Rate Prediction," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 449-71, June.
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  18. 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. [Downloadable!] (restricted)
  19. 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. [Downloadable!] (restricted)
  20. 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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  21. Inoue, Atsushi & Kilian, Lutz, 2006. "On the selection of forecasting models," Journal of Econometrics, Elsevier, vol. 130(2), pages 273-306, February. [Downloadable!] (restricted)
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