Asymptotic properties of high-order Yule-Walker estimates of the AR parameters of an ARMA time series

The high-order Yule-Walker equations are used to estimate the autoregressive parameters of an autoregressive moving-average time series. The asymptotic statistical properties of these estimates are derived. It is shown that they are asymptotically unbiased and normal, the covariance matrix of the limit distribution is derived. The special case of estimating the autoregressive parameters of a noise corrupted autoregressive series is also examined.