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Reality checks and nested forecast model comparisons

  • Todd E. Clark
  • Michael W. McCracken

This paper develops a novel and effective bootstrap method for simulating asymptotic critical values for tests of equal forecast accuracy and encompassing among many nested models. The bootstrap, which combines elements of fixed regressor and wild bootstrap methods, is simple to use. We first derive the asymptotic distributions of tests of equal forecast accuracy and encompassing applied to forecasts from multiple models that nest the benchmark model – that is, reality check tests applied to nested models. We then prove the validity of the bootstrap for these tests. Monte Carlo experiments indicate that our proposed bootstrap has better finite-sample size and power than other methods designed for comparison of non-nested models. We conclude with empirical applications to multiple-model forecasts of commodity prices and GDP growth.

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Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2010-032.

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Date of creation: 2010
Date of revision:
Handle: RePEc:fip:fedlwp:2010-032
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  1. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  2. Todd E. Clark & Michael W. McCracken, 2009. "Nested forecast model comparisons: a new approach to testing equal accuracy," Research Working Paper RWP 09-11, Federal Reserve Bank of Kansas City.
  3. Amit Goyal & Ivo Welch, 2003. "Predicting the Equity Premium with Dividend Ratios," Management Science, INFORMS, vol. 49(5), pages 639-654, May.
  4. Denton, Frank T, 1985. "Data Mining as an Industry," The Review of Economics and Statistics, MIT Press, vol. 67(1), pages 124-27, February.
  5. Gonçalves, Sílvia & KILIAN, Lutz, 2003. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Cahiers de recherche 01-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Yu-chin Chen & Kenneth Rogoff & Barbara Rossi, 2010. "Can Exchange Rates Forecast Commodity Prices?," Working Papers 10-07, Duke University, Department of Economics.
  7. Amit Goyal & Ivo Welch, 2004. "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction," Yale School of Management Working Papers amz2412, Yale School of Management, revised 01 Jan 2006.
  8. Lucio Sarno & Daniel L. Thornton & Giorgio Valente, 2004. "Federal funds rate prediction," Working Papers 2002-005, Federal Reserve Bank of St. Louis.
  9. 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.
  10. Yin-Wong Cheung & Menzie D. Chinn & Antonio Garcia-Pascual, 2005. "Empirical Exchange Rate Models of the Nineties: Are Any Fit to Survive?," Working Papers 122005, Hong Kong Institute for Monetary Research.
  11. Moench, Emanuel, 2008. "Forecasting the yield curve in a data-rich environment: A no-arbitrage factor-augmented VAR approach," Journal of Econometrics, Elsevier, vol. 146(1), pages 26-43, September.
  12. 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.
  13. Kirstin Hubrich, 2004. "Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?," Computing in Economics and Finance 2004 230, Society for Computational Economics.
  14. Kevin Hoover & Stephen J. Perez, 2003. "Data Mining Reconsidered: Encompassing And The General-To-Specific Approach To Specification Search," Working Papers 9727, University of California, Davis, Department of Economics.
  15. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  16. Jan J. J. Groen, 1999. "Long horizon predictability of exchange rates: Is it for real?," Empirical Economics, Springer, vol. 24(3), pages 451-469.
  17. Andreas Billmeier, 2004. "Ghostbusting: Which Output Gap Measure Really Matters?," IMF Working Papers 04/146, International Monetary Fund.
  18. Kenneth D. West & Todd Clark, 2006. "Approximately Normal Tests for Equal Predictive Accuracy in Nested Models," NBER Technical Working Papers 0326, National Bureau of Economic Research, Inc.
  19. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  20. Kilian, Lutz, 1999. "Exchange Rates and Monetary Fundamentals: What Do We Learn from Long-Horizon Regressions?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 491-510, Sept.-Oct.
  21. 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.
  22. Alexander W. Butler & Gustavo Grullon & James P. Weston, 2005. "Can Managers Forecast Aggregate Market Returns?," Journal of Finance, American Finance Association, vol. 60(2), pages 963-986, 04.
  23. Kirstin Hubrich & Kenneth D. West, 2008. "Forecast Evaluation of Small Nested Model Sets," NBER Working Papers 14601, National Bureau of Economic Research, Inc.
  24. Hendry, David F. & Hubrich, Kirstin, 2011. "Combining Disaggregate Forecasts or Combining Disaggregate Information to Forecast an Aggregate," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 216-227.
  25. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
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