Approaches for Identifying Continuous-Time AR Processes from Unevenly Sampled Data

Abstract

When identifying a continuous-time AR process from discrete-time data, an obvious approach is to replace the derivative operator in the continuous-time model by an approximation. In some cases, a linear regression model can then be formulated. The well-known least squares method would be very desirable to apply, since it enjoy good numerical properties and low computational complexity, in particular for fast or nonuniform sampling. The focus of this paper is the latter, i.e. nonuniform sampling. Two consistent least squares schemes for the case of unevenly sampled data are presented. The precise choice of derivative approximation turns out to be crucial.