Estimated arma model

Question

Problem: You have estimated the following ARMA(1,1) model for some time series data:

Yt = 0.21 + 1.32Y_t-1 + 0.58U_t-1 + U_t

Suppose that you have data for time to t-1, i.e. you know that Yt-1 = 3.4 and = -1.3

(a) Obtain forecasts for the series y for times t, t+1 and t+2 using the estimated ARMA model.

(b) If the actual values for the series turned out to be 4.1, 5.6 and 6.2 for t, t+1 and t+2, respectively, calculate the (out-of-sample) mean squared error.