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Tests of Equal Forecast Accuracy and Encompassing for Nested Models

Listed author(s):
  • Todd E. Clark

    ()

    (Federal Reserve Bank of Kansas City)

  • Michael McCracken

    ()

    (Louisiana State University)

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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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1999 with number 1241.

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Date of creation: 01 Mar 1999
Handle: RePEc:sce:scecf9:1241
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CEF99, Boston College, Department of Economics, Chestnut Hill MA 02467 USA

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