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On the selection of forecasting models

  • Inoue, Atsushi
  • Kilian, Lutz

It is standard in applied work to select forecasting models by ranking candidate models by their prediction mean square error (PMSE) in simulated ou-of-sample (SOOS) forecasts. Alternatively, forecast models may be selected using information criteria (IC). We compare the asymptotic and finite-sample properties of these methods in terms of their ability to minimize the true out-of-sample PMSE, allowing for possible misspecification of the forecast models under consideration. We first study a covariance stationary environment. We show that under suitable conditions the IC method will be consistent for the best approximating models among the candidate models. In contrast, under standard assumptions the SOOS method will select overparameterized models with positive probability, resulting in excessive finite-sample PMSEs. We also show that in the presence of unmodelled structural change both methods will be inadmissible in the sense that they may select a model with strictly higher PMSE than the best approximating models among the candidate models. JEL Classification: C22, C52, C53

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Paper provided by European Central Bank in its series Working Paper Series with number 0214.

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Date of creation: Feb 2003
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Handle: RePEc:ecb:ecbwps:20030214
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  1. Inoue, Atsushi & Kilian, Lutz, 2003. "On the Selection of Forecasting Models," CEPR Discussion Papers 3809, C.E.P.R. Discussion Papers.
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  7. Peter C.B. Phillips & Werner Ploberger, 1992. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Cowles Foundation Discussion Papers 1017, Cowles Foundation for Research in Economics, Yale University.
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  9. Bossaerts, Peter & Hillion, Pierre, 1999. "Implementing Statistical Criteria to Select Return Forecasting Models: What Do We Learn?," Review of Financial Studies, Society for Financial Studies, vol. 12(2), pages 405-28.
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  14. David Findley, 1991. "Counterexamples to parsimony and BIC," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(3), pages 505-514, September.
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  17. Marc Hallin & Mario Forni & Marco Lippi & Lucrezia Reichlin, 2003. "Do financial variables help forecasting inflation and real activity in the Euro area ?," ULB Institutional Repository 2013/2123, ULB -- Universite Libre de Bruxelles.
  18. James H. Stock & Mark W. Watson, 1998. "A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series," NBER Working Papers 6607, National Bureau of Economic Research, Inc.
  19. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, February.
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  21. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  22. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
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  26. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
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