Parameter Estimation for a Discretely Observed Integrated Diffusion Process

We consider the estimation of unknown parameters in the drift and diffusion coefficients of a one-dimensional ergodic diffusion <b>""X""</b> when the observation is a discrete sampling of the integral of <b>""X""</b> at times <b>""i""</b><b>Δ</b>,<b>""i""</b> &equals; <b>1</b>,&h ellip;,<b>""n""</b>. Assuming that the sampling interval tends to 0 while the total length time interval tends to infinity, we first prove limit theorems for functionals associated with our observations. We apply these results to obtain a contrast function. The associated minimum contrast estimators are shown to be consistent and asymptotically Gaussian with different rates for drift and diffusion coefficient parameters. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..