browsing Internet while preparing for my exam I came across an interesting exercise.
Consider a weakly stationary process $Y_t$ and $I_t=Y_t, Y_{t-1},...$ information available at time $t$.
Show that $E(Y_{t+h}|I_t)$ and $V(Y_{t+h}|I_t)$ converge to the moments of the stationary distributions, as the forecasting horizon $h$ increases.
Could you please help me show why this holds?