Bias reduction in the estimation of diffusion processes from discrete observations

Abstract

Abstract This work deals with the bias reduction of approximations to two known estimators of diffusion processes from discrete observations: the innovation and quasi-maximum likelihood estimators. The bias reduction is obtained by means of convergent approximations to the predictions for the first two moments of the innovation process associated to a continuous-discrete filter of minimum variance. For finite samples, the convergence of the approximate estimators to the exact one is proved when the error between the predictions and their approximations decreases no matter the time distance between observations. For an increasing number of observations, these approximate estimators are asymptotically normal distributed and their bias decreases when the above-mentioned error does it. A simulation study shows that, with respect to the conventional approximate estimators, the new ones significantly enhance the parameter estimation of the test equations. The new approximate estimators are intended for the recurrent practical situation in which a diffusion process should be identified from a reduced number of observations distant in time.