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Tests of equal forecast accuracy and encompassing for nested models

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  • Clark, Todd E.
  • McCracken, Michael W.

Abstract

Ashley, Granger, and Schmalensee (1980) and Diebold and Mariano (1995) suggest that forecast comparisons may be used to examine Granger causality. According to Ashley et al., if forecasts of y based on a VAR model in x and y are superior to those based on an AR model for y , then x carries information about y and hence causes y . Thus, this combination of tests can be viewed as a test for Granger causality. This paper examines both asymptotic and finite-sample properties of tests for equal accuracy and encompassing in the VAR vs. AR settings. The statistics considered include the Diebold-Mariano test for equal accuracy and the Chong and Hendry (1986) and Harvey et al. (1998) tests for encompassing. Because the Diebold-Mariano and Harvey et al. tests are designed for non-nested forecasts, they are asymptotically invalid when applied to forecasts from nested models. Asymptotically valid versions of the tests are also considered. Valid versions include an out-of-sample F -type statistic and a version of the Diebold-Mariano t -statistic developed in McCracken (1999), as well as a variant of the Harvey et al. encompassing statistic developed in this paper. The asymptotic tests developed by McCracken are extended to multi-step forecast horizons. Monte Carlo simulations show that using asymptotically invalid tests can produce misleading inferences in small samples. The simulations also indicate that out-of-sample F -type and encompassing tests can be more powerful than standard F -tests of causality.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 105 (2001)
Issue (Month): 1 (November)
Pages: 85-110

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Handle: RePEc:eee:econom:v:105:y:2001:i:1:p:85-110

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Web page: http://www.elsevier.com/locate/jeconom

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References

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  1. Todd E. Clark & Michael W. McCracken, 2000. "Tests of Equal Forecast Accuracy and Encompassing for Nested Models," Econometric Society World Congress 2000 Contributed Papers 0319, Econometric Society.
  2. Norman R. Swanson & Halbert White, 1995. "A Model Selection Approach to Real-Time Macroeconomic Forecasting Using Linear Models and Artificial Neural Networks," Macroeconomics 9503004, EconWPA.
  3. repec:att:wimass:9220 is not listed on IDEAS
  4. Ng, S. & Perron, P., 1994. "Unit Root Tests ARMA Models with Data Dependent Methods for the Selection of the Truncation Lag," Cahiers de recherche 9423, Universite de Montreal, Departement de sciences economiques.
  5. Francis X. Diebold & Glenn D. Rudebusch, 1989. "Forecasting output with the composite leading index: an ex ante analysis," Finance and Economics Discussion Series 90, Board of Governors of the Federal Reserve System (U.S.).
  6. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
  7. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  8. Jason Bram & Sydney Ludvigson, 1997. "Does consumer confidence forecast household expenditure?: A sentiment index horse race," Research Paper 9708, Federal Reserve Bank of New York.
  9. repec:att:wimass:9710 is not listed on IDEAS
  10. Ashley, Richard, 1998. "A new technique for postsample model selection and validation," Journal of Economic Dynamics and Control, Elsevier, vol. 22(5), pages 647-665, May.
  11. James H. Stock & Mark W. Watson, 1987. "Interpreting Evidence on Money-Income Causality," NBER Working Papers 2228, National Bureau of Economic Research, Inc.
  12. Norman R. Swanson, 2000. "An Out of Sample Test for Granger Causality," Econometric Society World Congress 2000 Contributed Papers 0362, Econometric Society.
  13. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
  14. 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.
  15. Chinn, Menzie D. & Meese, Richard A., 1995. "Banking on currency forecasts: How predictable is change in money?," Journal of International Economics, Elsevier, vol. 38(1-2), pages 161-178, February.
  16. repec:att:wimass:9417 is not listed on IDEAS
  17. 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.
  18. McCracken,M.W. & West,K.D., 2001. "Inference about predictive ability," Working papers 14, Wisconsin Madison - Social Systems.
  19. Stephen G. Cecchetti, 1995. "Inflation Indicators and Inflation Policy," NBER Working Papers 5161, National Bureau of Economic Research, Inc.
  20. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  21. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
  22. Joel T. Krueger & Kenneth N. Kuttner, 1995. "The Fed funds futures rate as a predictor of Federal Reserve policy," Working Paper Series, Macroeconomic Issues 95-4, Federal Reserve Bank of Chicago.
  23. Meese, R. & Rogoff, K., 1988. "Was It Real? The Exchange Rate-Interest Differential Ralation Over The Modern Floating-Rate Period," Working papers 368, Wisconsin Madison - Social Systems.
  24. Jeremy Berkowitz & Lorenzo Giorgianni, 2001. "Long-Horizon Exchange Rate Predictability?," The Review of Economics and Statistics, MIT Press, vol. 83(1), pages 81-91, February.
  25. West, Kenneth D, 2001. "Tests for Forecast Encompassing When Forecasts Depend on Estimated Regression Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 29-33, January.
  26. repec:cup:etheor:v:8:y:1992:i:4:p:489-500 is not listed on IDEAS
  27. Evans, Martin D. & Lyons, Richard K., 1999. "Order Flow and Exchange Rate Dynamics," Research Program in Finance, Working Paper Series qt0dh1c16w, Research Program in Finance, Institute for Business and Economic Research, UC Berkeley.
  28. 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.
  29. Kenneth D. West, 2000. "Encompassing Tests When No Model Is Encompassing," NBER Technical Working Papers 0256, National Bureau of Economic Research, Inc.
  30. S. Brock Blomberg & Gregory D. Hess, 1996. "Politics and exchange rate forecasts," Research Working Paper 96-02, Federal Reserve Bank of Kansas City.
  31. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  32. Todd E. Clark, 1996. "Finite-sample properties of tests for forecast equivalence," Research Working Paper 96-03, Federal Reserve Bank of Kansas City.
  33. Kilian, Lutz, 1999. "Exchange Rates and Monetary Fundamentals: What Do We Learn from Long-Horizon Regressions?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 491-510, Sept.-Oct.
  34. Douglas Staiger & James H. Stock & Mark W. Watson, 1997. "The NAIRU, Unemployment and Monetary Policy," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 33-49, Winter.
  35. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
  36. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
  37. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  38. 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.
  39. Ghysels, Eric & Hall, Alastair, 1990. "A Test for Structural Stability of Euler Conditions Parameters Estimated via the Generalized Method of Moments Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 355-64, May.
  40. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
  41. Amano, Robert A. & van Norden, Simon, 1995. "Terms of trade and real exchange rates: the Canadian evidence," Journal of International Money and Finance, Elsevier, vol. 14(1), pages 83-104, February.
  42. Diebold, Francis X. & Chen, Celia, 1996. "Testing structural stability with endogenous breakpoint A size comparison of analytic and bootstrap procedures," Journal of Econometrics, Elsevier, vol. 70(1), pages 221-241, January.
  43. Harvey, David I & Leybourne, Stephen J & Newbold, Paul, 1998. "Tests for Forecast Encompassing," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 254-59, April.
  44. Neil R. Ericsson, 1991. "Parameter constancy, mean square forecast errors, and measuring forecast performance: an exposition, extensions, and illustration," International Finance Discussion Papers 412, Board of Governors of the Federal Reserve System (U.S.).
  45. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 461-70, October.
  46. Hoffman, Dennis L & Pagan, Adrian R, 1989. "Post-Sample Prediction Tests for Generalized Method of Moments Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 51(3), pages 333-43, August.
  47. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  48. Francis X. Diebold & James M. Nason, 1989. "Nonparametric exchange rate prediction?," Finance and Economics Discussion Series 81, Board of Governors of the Federal Reserve System (U.S.).
  49. Mark, Nelson C, 1995. "Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability," American Economic Review, American Economic Association, vol. 85(1), pages 201-18, March.
  50. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  51. Nelson, Charles R, 1972. "The Prediction Performance of the FRB-MIT-PENN Model of the U.S. Economy," American Economic Review, American Economic Association, vol. 62(5), pages 902-17, December.
  52. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  53. Ashley, R & Granger, C W J & Schmalensee, R, 1980. "Advertising and Aggregate Consumption: An Analysis of Causality," Econometrica, Econometric Society, vol. 48(5), pages 1149-67, July.
  54. Swanson, N.R. & Ozyildirim, A. & Pisu, M., 1996. "A Comparison of Alternatove causality and Predictive Accuracy Tests in the presence of Integrated and Co-integrated Economic Variables," Papers 4-96-4, Pennsylvania State - Department of Economics.
  55. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  56. Mizrach, Bruce, 1992. "The distribution of the Theil U-statistic in bivariate normal populations," Economics Letters, Elsevier, vol. 38(2), pages 163-167, February.
  57. Lutkepohl, Helmut & Burda, Maike M., 1997. "Modified Wald tests under nonregular conditions," Journal of Econometrics, Elsevier, vol. 78(2), pages 315-332, June.
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