Exercise n. 2: Analyzing the time series Y(t), t=1,60, you have found that the following MA(2) model fits the data well:

Y(t) = e(t) + .2*e(t-1) -.3*e(t-2), var{e(t)} = 8.2.

Q5. Derive the average and the variance of Y(t) implied by this model

Q6. Derive cov{Y(t), Y(t-1)}

Q7. Derive the forecasting function implied by this model for periods 61, 62, 63.

Q8. Derive the variance of the forecasting errors for periods 61, 62 and 63.