We analyze in this paper the asymptotic behavior of the specification test of Aït-Sahalia (1996) for the stationary density of a diffusion process, but when the diffusion is not stationary. We consider integrated and explosive processes, as well as nearly integrated ones in the spirit of the local to unity analysis in classical unit root theory. We find that the behavior of the test predicted by the asymptotic distribution under an integrated process provides a better approximation to the small sample distribution of the test than that predicted by the asymptotic distribution under strict stationarity.
All Science Journal Classification (ASJC) codes
- Economics and Econometrics