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Tests of equal accuracy for nested models with estimated factors


  • Gonçalves, Sílvia
  • McCracken, Michael W.
  • Perron, Benoit


In this paper we develop asymptotics for tests of equal predictive ability between nested models when factor-augmented regressions are used to forecast. We provide conditions under which the estimation of the factors does not affect the asymptotic distributions developed in Clark and McCracken (2001) and McCracken (2007). This enables researchers to use the existing tabulated critical values when conducting inference despite the presence of estimated predictors. As an intermediate result, we derive the asymptotic properties of the principal components estimator over recursive windows. We provide simulation evidence on the finite sample effects of factor estimation and apply the tests to the case of forecasting excess returns to the S&P 500 Composite Index.

Suggested Citation

  • Gonçalves, Sílvia & McCracken, Michael W. & Perron, Benoit, 2017. "Tests of equal accuracy for nested models with estimated factors," Journal of Econometrics, Elsevier, vol. 198(2), pages 231-252.
  • Handle: RePEc:eee:econom:v:198:y:2017:i:2:p:231-252
    DOI: 10.1016/j.jeconom.2017.01.004

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    References listed on IDEAS

    1. Cheng, Xu & Hansen, Bruce E., 2015. "Forecasting with factor-augmented regression: A frequentist model averaging approach," Journal of Econometrics, Elsevier, vol. 186(2), pages 280-293.
    2. Shintani, Mototsugu, 2005. "Nonlinear Forecasting Analysis Using Diffusion Indexes: An Application to Japan," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 517-538, June.
    3. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    4. Gonçalves, Sílvia & Perron, Benoit, 2014. "Bootstrapping factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 182(1), pages 156-173.
    5. Adrian Pagan, 1986. "Two Stage and Related Estimators and Their Applications," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 517-538.
    6. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    7. Hjalmarsson, Erik, 2010. "Predicting Global Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(1), pages 49-80, February.
    8. 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.
    9. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    10. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    11. Matteo Ciccarelli & Benoît Mojon, 2010. "Global Inflation," The Review of Economics and Statistics, MIT Press, vol. 92(3), pages 524-535, August.
    12. Sydney C. Ludvigson & Serena Ng, 2009. "A Factor Analysis of Bond Risk Premia," NBER Working Papers 15188, National Bureau of Economic Research, Inc.
    13. Hofmann, Boris, 2009. "Do monetary indicators lead euro area inflation?," Journal of International Money and Finance, Elsevier, vol. 28(7), pages 1165-1181, November.
    14. Peter Reinhard Hansen & Allan Timmermann, 2015. "Equivalence Between Out‐of‐Sample Forecast Comparisons and Wald Statistics," Econometrica, Econometric Society, vol. 83, pages 2485-2505, November.
    15. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    16. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
    17. repec:taf:jnlbes:v:30:y:2012:i:1:p:53-66 is not listed on IDEAS
    18. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
    19. Elena Andreou & Eric Ghysels & Andros Kourtellos, 2013. "Should Macroeconomic Forecasters Use Daily Financial Data and How?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(2), pages 240-251, April.
    20. 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.
    21. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    22. Han, Xu & Inoue, Atsushi, 2015. "Tests For Parameter Instability In Dynamic Factor Models," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1117-1152, October.
    23. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
    24. Jennie Bai, 2010. "Equity premium predictions with adaptive macro indexes," Staff Reports 475, Federal Reserve Bank of New York.
    25. 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.
    26. Cem Cakmakli & Dick van Dijk, 2010. "Getting the Most out of Macroeconomic Information for Predicting Stock Returns and Volatility," Tinbergen Institute Discussion Papers 10-115/4, Tinbergen Institute.
    27. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    28. Jack Fosten, 2016. "Forecast evaluation with factor-augmented models," University of East Anglia School of Economics Working Paper Series 2016-05, School of Economics, University of East Anglia, Norwich, UK..
    29. Çakmaklı, Cem & van Dijk, Dick, 2016. "Getting the most out of macroeconomic information for predicting excess stock returns," International Journal of Forecasting, Elsevier, vol. 32(3), pages 650-668.
    30. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
    31. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
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    Cited by:

    1. Marine Carrasco & Barbara Rossi, 2016. "In-Sample Inference and Forecasting in Misspecified Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 313-338, July.
    2. Daniel Borup & Bent Jesper Christensen & Yunus Emre Ergemen, 2019. "Assessing predictive accuracy in panel data models with long-range dependence," CREATES Research Papers 2019-04, Department of Economics and Business Economics, Aarhus University.
    3. Fosten, Jack, 2017. "Confidence intervals in regressions with estimated factors and idiosyncratic components," Economics Letters, Elsevier, vol. 157(C), pages 71-74.
    4. Antoine A. Djogbenou, 2017. "Model Selection In Factor-augmented Regressions With Estimated Factors," Working Paper 1391, Economics Department, Queen's University.
    5. Daniel Borup & Martin Thyrsgaard, 2017. "Statistical tests for equal predictive ability across multiple forecasting methods," CREATES Research Papers 2017-19, Department of Economics and Business Economics, Aarhus University.

    More about this item


    Factor model; Out-of-sample forecasts; Recursive estimation;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection


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