Download Organizer: Ching-Shui Cheng - Department of Statistics and Applied

The 6th ICSA International Conference
21 - 23 July 2004, Singapore
On Non-parametric Specification Tests of Diffusion Models
Song Xi CHEN
Department of Statistics, Iowa State University and Department of Statistics and Applied
Probability, National University of Singapore.
We consider the use of the non-parametric kernel method for testing specification of
diffusion models pioneered in Ait-Sahaila (1996, {Review of Financial Studies}). A serious
doubt on the ability of the kernel method for testing diffusion models is cast in Pritsker
(1998, {Review of Financial Studies}), who observes severe size distortion of the test
proposed by Ait-Sahaila and finds in order for the test to have a correct size 2755 years of
data are required. In this talk, we show that the dramatic size distortion observed by
Pritsker (1998) is partly due to the use of the asymptotic normality of the test statistic
which is known to converge slowly even for independent observations. We reformulate
the test statistic of Ait-Sahaila (1996) by a version of the empirical likelihood coupled with
a bootstrap procedure. We also consider an empirical likelihood test for the transitional
density which, unlike a test based on a marginal density, is conclusive for diffusion
models. We demonstrate that the proposed test has reasonable size and power for
realistic sizes of observations, which indicates that the kernel method is a valid method
for testing specification of diffusion models.