Performance analysis of some methods fof identifying continuous-time autoregressive processes

Abstract

Identification of continuous-time AR processes by least squares and instrumental variables methods using discrete-time data in a ‘direct approach’ is considered. The derivatives are substituted by discrete-time differences, for example by replacing differentiation by a delta operator. In this fashion the model is casted into a (discrete-time) linear regression. In earlier work we gave sufficient conditions for the estimates to be close to their true values for large data sets and small sampling intervals. The purpose of this paper is to further analyse the statistical properties of the parameter estimates. We give expressions for the dominating bias term of the estimates, for a general linear estimator applied to the continuous-time autoregressive process. Further, we consider the asymptotic distribution of the estimates. It turns out to be Gaussian, and we characterise its covariance matrix, which has a simple form.