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Nested forecast model comparisons: a new approach to testing equal accuracy

  • Todd E. Clark
  • Michael W. McCracken

This paper develops bootstrap methods for testing whether, in a finite sample, competing out-of-sample forecasts from nested models are equally accurate. Most prior work on forecast tests for nested models has focused on a null hypothesis of equal accuracy in population basically, whether coefficients on the extra variables in the larger, nesting model are zero. We instead use an asymptotic approximation that treats the coefficients as non-zero but small, such that, in a finite sample, forecasts from the small model are expected to be as accurate as forecasts from the large model. Under that approximation, we derive the limiting distributions of pairwise tests of equal mean square error, and develop bootstrap methods for estimating critical values. Monte Carlo experiments show that our proposed procedures have good size and power properties for the null of equal finite-sample forecast accuracy. We illustrate the use of the procedures with applications to forecasting stock returns and inflation.

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Paper provided by Federal Reserve Bank of Kansas City in its series Research Working Paper with number RWP 09-11.

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Date of creation: 2009
Date of revision:
Handle: RePEc:fip:fedkrw:rwp09-11
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  1. Jan J. J. Groen, 1999. "Long horizon predictability of exchange rates: Is it for real?," Empirical Economics, Springer, vol. 24(3), pages 451-469.
  2. Todd E. Clark & Michael W. McCracken, 1999. "Tests of equal forecast accuracy and encompassing for nested models," Research Working Paper 99-11, Federal Reserve Bank of Kansas City.
  3. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October.
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  9. James H. Stock & Mark W.Watson, 2003. "Forecasting Output and Inflation: The Role of Asset Prices," Journal of Economic Literature, American Economic Association, vol. 41(3), pages 788-829, September.
  10. Todd E. Clark & Michael W. McCracken, 2009. "Combining Forecasts from Nested Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 303-329, 06.
  11. repec:oup:qjecon:v:125:y:2010:i:3:p:1145-1194 is not listed on IDEAS
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  13. Kilian, Lutz & Taylor, Mark P., 2003. "Why is it so difficult to beat the random walk forecast of exchange rates?," Journal of International Economics, Elsevier, vol. 60(1), pages 85-107, May.
  14. Clark, Todd E. & McCracken, Michael W., 2006. "The Predictive Content of the Output Gap for Inflation: Resolving In-Sample and Out-of-Sample Evidence," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(5), pages 1127-1148, August.
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  19. 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.
  20. repec:taf:jnlbes:v:30:y:2012:i:1:p:53-66 is not listed on IDEAS
  21. Rossi, Barbara & Giacomini, Raffaella, 2005. "How Stable is the Forecasting Performance of the Yield Curve for Outpot Growth?," Working Papers 05-08, Duke University, Department of Economics.
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  23. Michael Cooper & Huseyin Gulen, 2006. "Is Time-Series-Based Predictability Evident in Real Time?," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1263-1292, May.
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  29. Ferreira, Miguel A. & Santa-Clara, Pedro, 2011. "Forecasting stock market returns: The sum of the parts is more than the whole," Journal of Financial Economics, Elsevier, vol. 100(3), pages 514-537, June.
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