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 earlie r results relating the autoregressive coefficients to the set of posit ive parameters called residual variances ratios, we develop an iterati ve algorithm for computing the maximum likelihood estimator of the mod el, similar to one in the discrete-time case. A simple noniterative es timation method, which can be used to produce an initial estimate for the algorithm, is also proposed.