Finite-Sample Bias in the Yule-Walker Method of Autoregressive Estimation

摘要

Lagged-product autocorrelation estimates have a small triangular bias. Using that biased autocorrelation to compute an autoregressive model is called the Yule-Walker method of auto-regressive estimation. The method is asymptotically unbiased, but it can give a strongly distorted spectral model in finite samples. The bias distortion can even become significant in simple, non-extreme examples, where the reflection coefficients are not close to one in absolute value. A new objective measure will be presented to determine the smallest sample size for which the Yule-Walker bias becomes negligible if the autoregressive parameters are known. The autoregressive estimation method of Burg does not suffer from this bias and is to be preferred for spectral estimation and for estimation of the autocorrelation function in practice.