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Out-Of-Sample Comparisons of Overfit Models

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  • Calhoun, Gray

Abstract

This paper uses dimension asymptotics to study why overfit linear regression models should be compared out-of-sample; we let the number of predictors used by the larger model increase with the number of observations so that their ratio remains uniformly positive. Our analysis gives a theoretical motivation for using out-of-sample (OOS) comparisons: the DMW OOS test allows a forecaster to conduct inference about the expected future accuracy of his or her models when one or both is overfit. We show analytically and through Monte Carlo that standard full-sample test statistics can not test hypotheses about this performance. Our paper also shows that popular test and training sample sizes may give misleading results if researchers are concerned about overfit. We show that P 2 /T must converge to zero for theDMW test to give valid inference about the expected forecast accuracy, otherwise the test measures the accuracy of the estimates constructed using only the training sample. In empirical research, P is typically much larger than this. Our simulations indicate that using large values of P with the DMW test gives undersized tests with low power, so this practice may favor simple benchmark models too much.

Suggested Citation

  • Calhoun, Gray, 2014. "Out-Of-Sample Comparisons of Overfit Models," Staff General Research Papers Archive 32462, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:32462
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    File URL: http://www2.econ.iastate.edu/papers/p12462-2014-03-28.pdf
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    References listed on IDEAS

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    1. Clark, Todd E. & McCracken, Michael W., 2015. "Nested forecast model comparisons: A new approach to testing equal accuracy," Journal of Econometrics, Elsevier, vol. 186(1), pages 160-177.
    2. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    3. 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.
    4. Raffaella Giacomini & Barbara Rossi, 2009. "Detecting and Predicting Forecast Breakdowns," Review of Economic Studies, Oxford University Press, vol. 76(2), pages 669-705.
    5. Atsushi Inoue & Lutz Kilian, 2005. "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?," Econometric Reviews, Taylor & Francis Journals, vol. 23(4), pages 371-402.
    6. Clark, Todd E. & West, Kenneth D., 2006. "Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 155-186.
    7. Clark, Todd E. & McCracken, Michael W., 2012. "In-sample tests of predictive ability: A new approach," Journal of Econometrics, Elsevier, vol. 170(1), pages 1-14.
    8. Corradi, Valentina & Swanson, Norman R., 2004. "Some recent developments in predictive accuracy testing with nested models and (generic) nonlinear alternatives," International Journal of Forecasting, Elsevier, vol. 20(2), pages 185-199.
    9. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
    10. 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.
    11. Calhoun, Gray, 2011. "Hypothesis testing in linear regression when k/n is large," Journal of Econometrics, Elsevier, vol. 165(2), pages 163-174.
    12. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
    13. Chao, John & Corradi, Valentina & Swanson, Norman R., 2001. "Out-Of-Sample Tests For Granger Causality," Macroeconomic Dynamics, Cambridge University Press, vol. 5(04), pages 598-620, September.
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    Citations

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    Cited by:

    1. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, Elsevier.
    2. Yin, Anwen, 2015. "Forecasting and model averaging with structural breaks," ISU General Staff Papers 201501010800005727, Iowa State University, Department of Economics.
    3. Carlos Medel, 2017. "Forecasting Chilean inflation with the hybrid new keynesian Phillips curve: globalisation, combination, and accuracy," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 20(3), pages 004-050, December.
    4. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, Elsevier.
    5. Medel, Carlos A., 2015. "Forecasting Inflation with the Hybrid New Keynesian Phillips Curve: A Compact-Scale Global VAR Approach," MPRA Paper 67081, University Library of Munich, Germany.
    6. Travis J. Berge, 2014. "Forecasting Disconnected Exchange Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 713-735, August.

    More about this item

    Keywords

    Generalization Error; Forecasting; ModelSelection; t-test; Dimension Asymptotics;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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