Parameter estimation using Yule-Walker equations for a non-zero mean AR(p) process Suppose I want to find the coefficients $\phi_1,\phi_2$ of a non-zero mean AR(2) process $X_t$ using the calculated sample acvfs, and the sample mean is given as $\mu$. Can I still use the Yule-Walker estimator: i.e.
$$\Gamma_2\boldsymbol{\phi}=\boldsymbol{\gamma_2}$$ where $\Gamma_2 = [\gamma(i-j)]_{i,j=1}^{2}$, $\boldsymbol{\phi}=(\phi_1, \phi_2)'$, $\boldsymbol{\gamma}=(\gamma(1), \gamma(2))'$, $\gamma(h)$ is the sample acvf at lag $h$ and solve for $\boldsymbol{\phi}$? How to account for the fact that $X_t$ is non-zero mean?

Parameter estimation using Yule-Walker can proceed as follows in the case of a series $X_t$ with mean $\mu$. Form $Y_t=X_t-\mu$. Estimate $\hat\phi$ and $\hat\sigma^2$ using $Y_t$ as you normally would with any zero-mean series. Then to forecast $X_{t+h}$, you would just use $\hat Y_{t+h}$+$\mu$.
