Bootstrap specification tests for diffusion processes

摘要

This paper discusses specification tests for diffusion piocesscs In the one-dimensional case, our proposed test is closest to the nonparametric test of Ait-Sahalia (Rev Financ Stud 9 (1996) 385). However, we compare CDFs instead of densities In the multidimensional and/or multifactor case, our proposed test is based on comparison of the empirical CDF of actual data and the empirical CDF of simulated data. Asymptotically valid critical values are obtained using an empirical process version of the block bootstrap which accounts for parameter estimation eiror. An example based on a simple version of the Cox et al. (Econometrica 53 (1985) 385) model is outlined and related Monte Carlo experiments are carried out.