In 1982, T.W. Anderson wrote in a survey article on maximum likelihood estimation in autoregressive and moving average models: "A detailed study of the likelihood function ... will involve explicit expressions for the determinant and the components of the inverse of the covariance matrix. These are not available in the literature in closed form expressions for arbitrary finite orders. This study presents such a closed form and shows how profitable it is. Starting point is the formulation of the well-known ARMA equation in ...
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In 1982, T.W. Anderson wrote in a survey article on maximum likelihood estimation in autoregressive and moving average models: "A detailed study of the likelihood function ... will involve explicit expressions for the determinant and the components of the inverse of the covariance matrix. These are not available in the literature in closed form expressions for arbitrary finite orders. This study presents such a closed form and shows how profitable it is. Starting point is the formulation of the well-known ARMA equation in matrix form by using simple triangular matrices containing the parameters. The closed form of the ARMA covariance matrix is expressed as a function of these matrices arid is surprisingly simple. Its determinant and its inverse can easily be obtained, just like first and higher order derivatives with respect to its parameters. Detailed descriptions of efficient algorithms for the covariance matrix itself, its inverse and determinant are included. Of course, pure AR and MA models are contained in the general approach as special cases. Maximum likelihood estimation of exact ARMA models is investigated thoroughly, including first and second order derivatives of the likelihood function. A comparison of the maximum likelihood approach and the commonly used conditional least squares method for estimating ARMA parameters concludes this book."
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Add this copy of Maximum Likelihood Estimation of Exact Arma Models to cart. $25.00, like new condition, Sold by My Dead Aunt's Books rated 5.0 out of 5 stars, ships from Hyattsville, MD, UNITED STATES, published 1997 by Tilburg Uinversity Press.
