Asymptotic theory for linear diffusions under alternative sampling schemes

•Discuss three possibilities to make inference about the persistence parameter in diffusion models.•Develop the in-fill asymptotic distribution for the persistence parameter.•Show that the in-fill asymptotic distribution gives a more accurate approximation using simulated data.•Use the in-fill asymptotic distribution for unit root testing using real data.

The asymptotic distributions of the maximum likelihood estimator of the persistence parameter are developed in a linear diffusion model under three sampling schemes, long-span, in-fill and double. Simulations suggest that the in-fill asymptotic distribution gives a more accurate approximation to the finite sample distribution than the other two distributions. An empirical application highlights the difference in unit root testing based on the alternative asymptotic distributions.