Let us say one is working with a state-space model for the purpose of (short term) forecasting of an underlying (say FX rates), now for model estimation from historical data, how far back should one look? Say if we do a maximum likelihood estimation and get two different estimates using window sizes n1 and n2 and therefore two different forecasts, would it make any sense to calculate the final forecast as a weighted average of the individual forecasts? If our log likelihood values are L(n1) and L(n2), I was thinking of the following weighing scheme: w1 ~ Exp(L1/n1) and w2 ~ Exp(L2/n2), of course renormalized. By extension, the next question is how many look back windows can one use (optimally)?