The Acf Is Clearly Declining Very Slowly in This Case

Multiple Choice

The acf is clearly declining very slowly in this case, which is consistent with their being an autoregressive part to the appropriate model. The pacf is clearly significant for lags one and two, but the question is does it them become insignificant for lags 2 and 4, indicating an AR(2) process, or does it remain significant, which would be more consistent with a mixed ARMA process? Well, given the huge size of the sample that gave rise to this acf and pacf, even a pacf value of 0.001 would still be statistically significant. Thus an ARMA process is the most likely candidate, although note that it would not be possible to tell from the acf and pacf which model from the ARMA family was more appropriate. The DGP for the data that generated this plot was y_t = 0.9 y_(t-1) - 0.3 u_(t-1) + u_t.
-Consider the following AR(2) model. What is the optimal 2-step ahead forecast for y if all information available is up to and including time t, if the values of y at time t, t-1 and t-2 are -0.3, 0.4 and -0.1 respectively, and the value of u at time t-1 is 0.3? y_t = -0.1 + 0.75y_t-1 - 0.125y_t-2 + u_t

A) -0.1
B) 0.27
C) -0.34
D) 0.30