Maximum likelihood estimation for continuous-time autoregressive models by relaxation on residual variances ratio parameters

In this paper we derive an explicit expression for the log likelihood function of a continuous-time autoregressive model. Then, using earlier results relating the autoregressive coefficients to the set of positive parameters called residual variances ratios, we develop an iterative algorithm for computing the maximum likelihood estimator of the model, similar to one in the discrete-time case. A simple noniterative estimation method, which can be used to produce an initial estimate for the algorithm, is also proposed.