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Out-Of-Sample Comparisons of Overfit Models

Listed author(s):
  • 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://www2.econ.iastate.edu/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 Archive with number 32462.

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Date of creation: 28 Mar 2014
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. 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.
  2. Giacomini, Raffaella & White, Halbert, 2003. "Tests of Conditional Predictive Ability," University of California at San Diego, Economics Working Paper Series qt5jk0j5jh, Department of Economics, UC San Diego.
  3. 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.
  4. Rossi, Barbara & Giacomini, Raffaella, 2006. "Detecting and Predicting Forecast Breakdowns," Working Papers 06-01, Duke University, Department of Economics.
  5. Inoue, Atsushi & Kilian, Lutz, 2002. "In-sample or out-of-sample tests of predictability: which one should we use?," Working Paper Series 0195, European Central Bank.
  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. 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.
  8. Valentina Corradi & Norman Swanson, 2003. "Some Recent Developments in Predictive Accuracy Testing With Nested Models and (Generic) Nonlinear Alternatives," Departmental Working Papers 200316, Rutgers University, Department of Economics.
  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, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers Archive 32216, Iowa State University, Department of Economics.
  12. Kenneth D. West & Todd Clark, 2006. "Approximately Normal Tests for Equal Predictive Accuracy in Nested Models," NBER Technical Working Papers 0326, National Bureau of Economic Research, Inc.
  13. Inoue, Atsushi & Kilian, Lutz, 2003. "On the selection of forecasting models," Working Paper Series 0214, European Central Bank.
  14. 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.
  15. Amit Goyal & Ivo Welch, 2004. "A Comprehensive Look at the Empirical Performance of Equity Premium Prediction," Yale School of Management Working Papers amz2412, Yale School of Management, revised 01 Jan 2006.
  16. Stanislav Anatolyev, 2007. "Inference about predictive ability when there are many predictors," Working Papers w0096, Center for Economic and Financial Research (CEFIR).
  17. Zeileis, Achim, 2004. "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i10).
  18. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  19. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
  20. 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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