In this paper, we derive an asymptotic closed--form expression for the error bound on extrapolation of doubly selective mobile MIMO wireless channels. The bound shows the relationship between the prediction error and system design parameters such as bandwidth, number of antenna elements, and number of frequency and temporal pilots, thereby providing useful insights into the effects of these parameters on prediction performance. Numerical simulations show that the asymptotic bound provides a good approximation to previously derived bounds while eliminating the need for repeated computation and dependence on channel parameters such as angles of arrival and departure, delays and Doppler shifts.