I am trying to get an intuitive understanding of Burg's method for estimation the coefficients of an AR-model. Say we have an AR(1)-process with
\begin{equation*} X_t = a X_{t-1} + \varepsilon_t \end{equation*}
Given some sample $\{X_t\}_0^N$ Burg's method implies we should find the coefficient $a$ which minimize both the forward and the backward prediction error
\begin{equation*} \sum_{t=1}^N | X_t - a X_{t-1}|^2 + \sum_{t=0}^{N-1} | X_{t} - a X_{t+1}|^2 \end{equation*}
Why is this a valid objective? Why would we include the backward prediction error given the model?
