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

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+