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The modified Yule-Walker (MYW) equations are often used to estimate the autoregressive parameters of time series. The asymptotic estimation error variance of these parameters can be computed using a formula developed for the instrumental variable method. The performance of the MYW estimator is studied by evaluating this formula for different signal-to-noise ratios and process bandwidths, as a function of the number of equations used by the estimator. The Cramer-Rao lower bound for the estimation error variance is computed for comparison. The optimally weighted MYW estimator is briefly discussed.