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Out-Of-Sample Comparisons of Overfit Models

  • Calhoun, Gray

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.

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File URL: http://www.econ.iastate.edu/sites/default/files/publications/papers/p12462-2014-03-28.pdf
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Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 32462.

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Date of creation: 28 Mar 2014
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Handle: RePEc:isu:genres:32462
Contact details of provider: Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
Web page: http://www.econ.iastate.edu
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  1. 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.
  2. Todd E. Clark & Michael McCracken, 1999. "Tests of Equal Forecast Accuracy and Encompassing for Nested Models," Computing in Economics and Finance 1999 1241, Society for Computational Economics.
  3. 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.
  4. Giacomini, Raffaella & Rossi, Barbara, 2006. "Detecting and predicting forecast breakdowns," Working Paper Series 0638, European Central Bank.
  5. Inoue, Atsushi & Kilian, Lutz, 2006. "On the selection of forecasting models," Journal of Econometrics, Elsevier, vol. 130(2), pages 273-306, February.
  6. 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.
  7. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
  8. Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
  9. Todd E. Clark & Michael W. McCracken, 2009. "In-sample tests of predictive ability: a new approach," Working Papers 2009-051, Federal Reserve Bank of St. Louis.
  10. de Jong, R.M. & Davidson, J., 1996. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Discussion Paper 1996-52, Tilburg University, Center for Economic Research.
  11. Achim Zeileis, . "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, American Statistical Association, vol. 11(i10).
  12. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  13. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
  14. 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.
  15. Todd E. Clark & Michael W. McCracken, 2009. "Nested forecast model comparisons: a new approach to testing equal accuracy," Working Papers 2009-050, Federal Reserve Bank of St. Louis.
  16. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  17. Calhoun, Gray, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers 32216, Iowa State University, Department of Economics.
  18. Stanislav Anatolyev, 2007. "Inference about predictive ability when there are many predictors," Working Papers w0096, Center for Economic and Financial Research (CEFIR).
  19. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(03), pages 353-367, June.
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