Suppose that \(Y_{t}\) follows the \(\operatorname{AR}(p)\) model \(Y_{t}=\beta_{0}+\beta_{1} Y_{t-1}+\cdots+\beta_{p} Y_{t-p}+\) \(u_{t}\), where \(E\left(u_{t} \mid Y_{t-1}, Y_{t-2}, \ldots\right)=0\). Let \(Y_{t+h \mid t}=E\left(Y_{t+h} \mid Y_{t}, Y_{t-1}, \ldots\right)\). Show that \(Y_{t+h \mid t}=\beta_{0}+\beta_{1} Y_{t-1+h \mid t}+\cdots+\beta_{p} Y_{t-p+h \mid t}\) for \(h>p\).