On the relation between triangular matrix decomposition and linear prediction

It is shown that the coefficients of linear prediction for a random process and the prediction error variances are related to the covariance matrix through triangular decomposition. In particular, if the covariance matrix is written in the product form LDL^*where L is lower triangular with unit diagonal and D is diagonal, then the rows of L^-1are the coefficients of linear prediction and the elements of D are the prediction error variances.