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

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  • Todd E. Clark
  • Michael W. McCracken

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:fip:fedkrw:rwp09-11
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    Cited by:

    1. Roberto Casarin & Stefano Grassi & Francesco Ravazzolo & Herman K. van Dijk, 2015. "Dynamic predictive density combinations for large data sets in economics and finance," Working Paper 2015/12, Norges Bank.
    2. Kang, Wensheng & Ratti, Ronald A. & Vespignani, Joaquin L., 2016. "The implications of liquidity expansion in China for the US dollar," Globalization and Monetary Policy Institute Working Paper 264, Federal Reserve Bank of Dallas.
    3. Bjørnland, Hilde C. & Ravazzolo, Francesco & Thorsrud, Leif Anders, 2017. "Forecasting GDP with global components: This time is different," International Journal of Forecasting, Elsevier, vol. 33(1), pages 153-173.
    4. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, Elsevier.
    5. Calhoun, Gray, 2014. "Out-Of-Sample Comparisons of Overfit Models," Staff General Research Papers Archive 32462, Iowa State University, Department of Economics.
    6. Alquist, Ron & Kilian, Lutz & Vigfusson, Robert J., 2013. "Forecasting the Price of Oil," Handbook of Economic Forecasting, Elsevier.
    7. Boriss Siliverstovs, 2017. "Short-term forecasting with mixed-frequency data: a MIDASSO approach," Applied Economics, Taylor & Francis Journals, vol. 49(13), pages 1326-1343, March.
    8. Francesco Ravazzolo & Philip Rothman, 2013. "Oil and U.S. GDP: A Real‐Time Out‐of‐Sample Examination," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(2-3), pages 449-463, March.
    9. repec:eee:intfor:v:33:y:2017:i:3:p:618-626 is not listed on IDEAS
    10. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Common Drifting Volatility in Large Bayesian VARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 375-390, July.
    11. Nikolsko-Rzhevskyy, Alex & Prodan, Ruxandra, 2012. "Markov switching and exchange rate predictability," International Journal of Forecasting, Elsevier, vol. 28(2), pages 353-365.
    12. Kang, Wensheng & Ratti, Ronald A. & Vespignani, Joaquin L., 2016. "The implications of monetary expansion in China for the US dollar," Journal of Asian Economics, Elsevier, vol. 46(C), pages 71-84.
    13. Hossein Hassani & Emmanuel Sirimal Silva, 2015. "A Kolmogorov-Smirnov Based Test for Comparing the Predictive Accuracy of Two Sets of Forecasts," Econometrics, MDPI, Open Access Journal, vol. 3(3), pages 1-20, August.
    14. Kichian, Maral & Rumler, Fabio, 2014. "Forecasting Canadian inflation: A semi-structural NKPC approach," Economic Modelling, Elsevier, vol. 43(C), pages 183-191.
    15. Arai, Natsuki, 2014. "Using forecast evaluation to improve the accuracy of the Greenbook forecast," International Journal of Forecasting, Elsevier, vol. 30(1), pages 12-19.
    16. Todd E. Clark & Taeyoung Doh, 2011. "A Bayesian evaluation of alternative models of trend inflation," Research Working Paper RWP 11-16, Federal Reserve Bank of Kansas City.
    17. Todd E. Clark & Michael W. McCracken, 2010. "Testing for unconditional predictive ability," Working Papers 2010-031, Federal Reserve Bank of St. Louis.
    18. Lutz Kilian & Robert J. Vigfusson, 2013. "Do Oil Prices Help Forecast U.S. Real GDP? The Role of Nonlinearities and Asymmetries," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 78-93, January.
    19. Raffaella Giacomini & Barbara Rossi, 2013. "Forecasting in macroeconomics," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 17, pages 381-408 Edward Elgar Publishing.
    20. Todd E. Clark & Michael W. McCracken, 2010. "Reality checks and nested forecast model comparisons," Working Papers 2010-032, Federal Reserve Bank of St. Louis.
    21. Faust, Jon & Wright, Jonathan H., 2013. "Forecasting Inflation," Handbook of Economic Forecasting, Elsevier.
    22. Guérin, Pierre & Maurin, Laurent & Mohr, Matthias, 2015. "Trend-Cycle Decomposition Of Output And Euro Area Inflation Forecasts: A Real-Time Approach Based On Model Combination," Macroeconomic Dynamics, Cambridge University Press, vol. 19(02), pages 363-393, March.
    23. repec:bla:obuest:v:79:y:2017:i:1:p:101-123 is not listed on IDEAS
    24. Blasques, F. & Koopman, S.J. & Mallee, M. & Zhang, Z., 2016. "Weighted maximum likelihood for dynamic factor analysis and forecasting with mixed frequency data," Journal of Econometrics, Elsevier, vol. 193(2), pages 405-417.

    More about this item

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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