Continuous time Gaussian Autoregression

The problem of tting continuous time autoregressions linear and non linear to closely and regularly spaced data is considered For the linear case Jones and Bergstrom used state space representations to compute exact maximum likelihood estimators and Phillips did so by tting an appropriate discrete time ARMA process to the data In this paper we use exact conditional maximum likelihood estimators for the continuously observed process to derive ap proximate maximum likelihood estimators based on the closely spaced discrete ob servations We do this for both linear and non linear autoregressions and indicate how the method can be modi ed also to deal with non uniformly but closely spaced data Examples are given to indicate the accuracy of the procedure