TESTING THE PARAMETRIC SPECIFICATION OF THE DIFFUSION FUNCTION IN A DIFFUSION PROCESS

Abstract

A new consistent test is proposed for the parametric specification of the diffusion function in a diffusion process without any restrictions on the functional form of the drift function. The data are assumed to be sampled discretely in a time interval that can be fixed or lengthened to infinity. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric diffusion function is correctly specified. Monte Carlo simulations are conducted to examine the finite-sample performance of the test, revealing that the test has good size and power.The author is grateful to Yacine Aït-Sahalia, John Knight, Oliver Linton (the co-editor), Greg Tkacz, Jun Yang, and three anonymous referees for helpful comments and suggestions. He also thanks seminar participants at the Bank of Canada, the 2004 Semiparametrics Conference in Rio de Janeiro, and the 2005 Econometric Study Group in Bristol. The views expressed in this paper are those of the author. No responsibility for them should be attributed to the Bank of Canada.

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