TIME SERIES AND THE ALGEBRAIC MATRIX RICCATI EQUATION

Abstract

One way of modelling certain kinds of time series is via the Yule-Walker equations. These are a set of (over-determined) linear equations for estimating the parameters in the models. The coefficients in these equations are estimates, obtained from the data, of the autocorrelations. In this paper two ways of solving the Yule-Walker equations are considered. The first is the well known method using the pseudo-inverse and the second uses the algebraic matrix Riccati equation. A number of numerical examples are used to illustrate and compare the two different approaches.