Autoregressive model#Yule-Walker equations

Named after Gilbert Walker and George Udny Yule Yule-Walker equations are used in the statistics, more precisely, the time series analysis, to estimate the parameters of AR (MA ) processes. They establish a connection between auto-regression coefficients and the Autokovarianzfolge the process.

The equations

Be a stationary autoregressive process of order p, ie, where is white noise, the Autokovarianzfolge. Then the Yule- Walker equations are valid:

Applications

With the above equations, then the following can be derived estimate for the parameters of the process: Let the (estimated ) covariance matrix of the process, as well as further. Then

A consistent estimator for, which almost certainly exists because of the almost certain positive definiteness of the correlation matrix.