A simple iterative algorithm is proposed for obtaining the maximum‐likelihood estimates (m.l.e.) of the parameters of the symmetric Toeplitz or Laurent correlation matrix. A numerical example based on real‐life data is provided to illustrate the computation involved in the estimation and to demonstrate the feasibility of the proposed algorithm. This paper also provides expression in explicit form for the computation of the asymptotic dispersion matrix of the MLE. For comparative purposes, the Toeplitz correlation hypothesis as also other structural hypotheses have been tested and the results are discussed. The use of the proposed method in estimating the elements of Σ in the first step and then the possibility of using this estimated Σ for deriving a generalized least square estimate of the regression coefficients is pointe