Yule–Walker estimator for an autoregressive process of order one
= Yule–Walker estimator for an autoregressive process of order one
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{title2=$\widehat\phi_{YW}=\widehat\rho(1)$}
For $X_t-\mu=\phi(X_{t-1}-\mu)+\varepsilon_t$, the <autocovariance> equation is $\gamma(1)=\phi\gamma(0)$. Replacing both autocovariances by sample sums divided by the same $n$ yields $\widehat\phi_{YW}=\widehat\gamma(1)/\widehat\gamma(0)$, the lag-one <sample autocorrelation function>.