Yule-Walker Estimation for the Moving-Average Model

On the noise-compensated Yule-Walker equations

Recently a method of estimating the parameters of an AR(p) random process based on measurements corrupted by additive white noise was described. The method involves solving a matrix pencil, called the Noise-Compensated Yule-Walker (NCYW) equations, for the AR parameters and the variance of the measurement noise. In this correspondence we give a necessary and sufficient condition for there to ex...

Nonparametric Estimation in the Model of Moving Average

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

Lagged-product autocorrelation estimates have a small triangular bias. However, using them to compute an autoregressive model with the Yule-Walker method can give a strongly distorted spectral model in finite samples. The distortion is shown for examples where the reflection coefficients are not very close to one in absolute value. It will disappear asymptotically. An objective measure is prese...

Finite-Sample Bias Propagation in Autoregressive Estimation With the Yule-Walker Method

The Yule–Walker (YW) method for autoregressive (AR) estimation uses lagged-product (LP) autocorrelation estimates to compute an AR parametric spectral model. The LP estimates only have a small triangular bias in the estimated autocorrelation function and are asymptotically unbiased. However, using them in finite samples with the YW method for AR estimation can give a strong distortion in the we...

Solutions of Yule-Walker equations for singular AR processes

A study is presented on solutions of the Yule-Walker equations for singular AR processes that are stationary outputs of a given AR system. If the Yule-Walker equations admit more than one solution and the order of the AR system is no less than two, the solution set includes solutions which define unstable AR systems. The solution set also includes one solution, the minimal norm solution, which ...