Two recursive estimates of autoregressive models based on maximum likelihood

Estimates for autoregressive models are obtained by approximating the maximum likelihood estimates in two ways. A recursive algorithm for computing the resulting estimates for increasing model orders is presented. To calculate a pth order estimate 0(p 2 ) arithmetic operations are required; hence for high order model fitting, the method is more economical than standard solutions using Gaussian elimination, for example. The Levinson-Durbin recursions for the Yule-Walker estimates can be regarded as a special case of the algorithm presented here.