The Yule–Walker equations as a weighted least-squares problem and the association with tapering

ABSTRACT

A common method for estimating the time-domain parameters of an autoregressive process is to use the Yule–Walker equations. Tapering has been shown intuitively and proven theoretically to reduce the bias of the periodogram in the frequency domain, but the intuition for the similar bias reduction in the time-domain estimates has been lacking. We provide insightful reasoning for why tapering reduces the bias in the Yule–Walker estimates by showing them to be equivalent to a weighted least-squares problem. This leads to the derivation of an optimal taper which behaves similarly to commonly used tapers.

Keywords:

• Autoregression
• Taper
• Weighted least squares
• Yule–Walker

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M10
• 91B84