CONSISTENT MODEL SPECIFICATION TESTS

Yanqin Fan and Qi Li

Econometric Theory, 2000, vol. 16, issue 06, pages 1016-1041

Abstract: We point out the close relationship between the integrated conditional moment tests in Bierens (1982, Journal of Econometrics 20, 105 134) and Bierens and Ploberger (1997, Econometrica 65, 1129 1152) with the complex-valued exponential weight function and the kernel-based tests in H rdle and Mammen (1993, Annals of Statistics 21, 1926 1947), Li and Wang (1998, Journal of Econometrics 87, 145 165), and Zheng (1996, Journal of Econometrics 75, 263 289). It is well established that the integrated conditional moment tests of Bierens (1982) and Bierens and Ploberger (1997) are more powerful than kernel-based nonparametric tests against Pitman local alternatives. In this paper we analyze the power properties of the kernel-based tests and the integrated conditional moment tests for a sequence of singular local alternatives, and show that the kernel-based tests can be more powerful than the integrated conditional moment tests for these singular local alternatives. These results suggest that integrated conditional moment tests and kernel-based tests should be viewed as complements to each other. Results from a simulation study are in agreement with the theoretical results.

Date: 2000
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