We present an approach to estimate the parameters of an autoregressive model. An exact formula of the inverse covariance matrix of an autoregressive stochastic process is obtained using the Lv and Huang explicit inverse of the Toeplitz matrix [13]. Thereafter, we establish that the log likelihood function of the process is identical to that obtained by the decomposition of Choleski. Then we derive the maximum likelihood estimate and study through simulation the asymptotic properties of the estimators. It is shown that the statistical properties of the estimated parameters are good using the proposed inverse covariance matrix. We compare our estimate to the classical estimate.

Toeplitz matrix, autoregressive process, simulation, Cholesky decomposition, Levinson-Durbin algorithm.