New insights into the high-order Yule-Walker equations

Some new analytical results on the high-order Yule-Walker (HOYW) equations are presented. A simple singularity condition for the high-order autocorrelation matrix is found which makes it possible to determine situations where application of the HOYW equations could be especially unsuitable. It is also shown that using the HOYW equations is equivalent to performing conventional noise compensation in the main diagonal of the low-order autocorrelation matrix. This is in connection with the possibility of matching a given set of (the first) 2M+1 autocorrelation estimates to a noisy autoregressive process of order M