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Encompassing Tests When No Model Is Encompassing

  • Kenneth D. West

This paper considers regression-based tests for encompassing, when none of the models under consideration encompasses all the other models. For both in- and out-of-sample applications, I derive asymptotic distributions and propose feasible procedures to construct confidence intervals and test statistics. Procedures that are asymptotically valid under the null of encompassing (e.g., Davidson and MacKinnon (1981)) can have large asymptotic and finite sample distortions. Simulations indicate that the proposed procedures can work well in samples of size typically available, though the divergence between actual and nominal confidence interval coverage sometimes is large.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0256.

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Date of creation: Jun 2000
Date of revision:
Publication status: published as West, Kenneth D. "Tests For Forecast Encompassing When Forecasts Depend On Estimated Regression," Journal of Business and Economic Statistics, 2001, v19(1,Jan), 29-33.
Handle: RePEc:nbr:nberte:0256
Note: TWP
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  1. Adrian R. Pagan & G. William Schwert, 1989. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
  2. Russell Davidson & James G. MacKinnon, 1980. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Working Papers 378, Queen's University, Department of Economics.
  3. Ericsson, Neil R., 1992. "Parameter constancy, mean square forecast errors, and measuring forecast performance: An exposition, extensions, and illustration," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 465-495, August.
  4. Ronald L. Cooper, 1972. "The Predictive Performance of Quarterly Econometric Models of the United States," NBER Chapters, in: Econometric Models of Cyclical Behavior, Volumes 1 and 2, pages 813-947 National Bureau of Economic Research, Inc.
  5. West, Kenneth D & McCracken, Michael W, 1998. "Regression-Based Tests of Predictive Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 817-40, November.
  6. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  7. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-84, September.
  8. McAleer, Michael, 1995. "The significance of testing empirical non-nested models," Journal of Econometrics, Elsevier, vol. 67(1), pages 149-171, May.
  9. Ericsson, Neil R & Marquez, Jaime, 1993. "Encompassing the Forecasts of U.S. Trade Balance Models," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 19-31, February.
  10. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
  11. Godfrey, L. G., 1998. "Tests of non-nested regression models some results on small sample behaviour and the bootstrap," Journal of Econometrics, Elsevier, vol. 84(1), pages 59-74, May.
  12. Robert F. Engle & Che-Hsiung Hong & Alex Kane, 1990. "Valuation of Variance Forecast with Simulated Option Markets," NBER Working Papers 3350, National Bureau of Economic Research, Inc.
  13. Diebold, Francis X., 1989. "Forecast combination and encompassing: Reconciling two divergent literatures," International Journal of Forecasting, Elsevier, vol. 5(4), pages 589-592.
  14. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  15. Godfrey, L. G. & Pesaran, M. H., 1983. "Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence," Journal of Econometrics, Elsevier, vol. 21(1), pages 133-154, January.
  16. Chong, Yock Y & Hendry, David F, 1986. "Econometric Evaluation of Linear Macro-Economic Models," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 671-90, August.
  17. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  18. Fair, Ray C & Shiller, Robert J, 1990. "Comparing Information in Forecasts from Econometric Models," American Economic Review, American Economic Association, vol. 80(3), pages 375-89, June.
  19. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-78, May.
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