On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

Abstract

In this work, we investigate the relationship between continuous-time autoregressive (AR) models and their sampled version. We consider uniform sampling and derive criteria for uniquely determining the continuous-time parameters from sampled data; the model order is assumed to be known. We achieve this by removing a set of measure zero from the collection of all AR models and by investigating the asymptotic behavior of the remaining set of autocorrelation functions. We provide necessary and sufficient conditions for uniqueness of general AR models, and we demonstrate the usefulness of this result by considering particular examples. We further exploit our theory and introduce an estimation algorithm that recovers continuous-time AR parameters from sampled data, regardless of the sampling interval. We demonstrate the usefulness of our algorithm for various Gaussian and non-Gaussian AR processes.