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Tests of equal forecast accuracy for overlapping models


  • Todd E. Clark
  • Michael W. McCracken


This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy when the models being compared are overlapping in the sense of Vuong (1989). Two models are overlapping when the true model contains just a subset of variables common to the larger sets of variables included in the competing forecasting models. We consider an out-of-sample version of the two-step testing procedure recommended by Vuong but also show that an exact one-step procedure is sometimes applicable. When the models are overlapping, we provide a simple-to-use fixed regressor wild bootstrap that can be used to conduct valid inference. Monte Carlo simulations generally support the theoretical results: the two-step procedure is conservative while the one-step procedure can be accurately sized when appropriate. We conclude with an empirical application comparing the predictive content of credit spreads to growth in real stock prices for forecasting U.S. real GDP growth.

Suggested Citation

  • Todd E. Clark & Michael W. McCracken, 2011. "Tests of equal forecast accuracy for overlapping models," Working Paper 1121, Federal Reserve Bank of Cleveland.
  • Handle: RePEc:fip:fedcwp:1121

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    References listed on IDEAS

    1. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    2. 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.
    3. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    4. Wright, Jonathan H. & Zhou, Hao, 2009. "Bond risk premia and realized jump risk," Journal of Banking & Finance, Elsevier, vol. 33(12), pages 2333-2345, December.
    5. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
    6. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    7. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    8. Wegener, Christian & von Nitzsch, Rüdiger & Cengiz, Cetin, 2010. "An advanced perspective on the predictability in hedge fund returns," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2694-2708, November.
    9. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
    10. Randi Næs & Johannes A. Skjeltorp & Bernt Arne Ødegard, 2008. "Liquidity and the business cycle," Working Paper 2008/11, Norges Bank.
    11. Faust, Jon & Rogers, John H & Wright, Jonathan H, 2005. "News and Noise in G-7 GDP Announcements," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 403-419, June.
    12. Fornari Fabio & Mele Antonio, 2013. "Financial Volatility and Economic Activity," Journal of Financial Management, Markets and Institutions, Società editrice il Mulino, issue 2, pages 155-198, December.
    13. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
    14. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
    15. Robert Rich & Jason Bram & Andrew Haughwout & James Orr & Rae Rosen & Rebecca Sela, 2005. "Using Regional Economic Indexes to Forecast Tax Bases: Evidence from New York," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 627-634, November.
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    Cited by:

    1. repec:eee:intfor:v:33:y:2017:i:3:p:618-626 is not listed on IDEAS
    2. Brent Meyer & Saeed Zaman, 2013. "It’s not just for inflation: The usefulness of the median CPI in BVAR forecasting," Working Paper 1303, Federal Reserve Bank of Cleveland.
    3. repec:oup:biomet:v:103:y:2016:i:4:p:905-914. is not listed on IDEAS
    4. Isao Ishida & Virmantas Kvedaras, 2015. "Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 1-53, January.

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