An asymptotic analysis of likelihood-based diffusion model selection using high frequency data

We provide a new asymptotic analysis of model selection procedure that compares likelihoods of two candidate diffusion models. Our asymptotic analysis relies on two dimensional asymptotic expansions with shrinking sampling interval Δ and increasing sampling span T, and clarifies the different roles of drift and diffusion functions in the selection of diffusion models. In particular, we show that the model with superior diffusion function specification is always preferred to the competing model regardless of their drift specifications if Δ is sufficiently small relative to T. The specifications of drift functions matter only when the models have an identical diffusion specification.