The following ARIMA model has been fit to a time series: a. Suppose that we are at the end of time period T = 100 and we know that the observed forecast error for period 100 was 0.5 and for period 99...

The following ARIMA model has been fit to a time series:

a. Suppose that we are at the end of time period
T
= 100 and we know that the observed forecast error for period 100 was 0.5 and for period 99 we know that the observed forecast error was -0.8. Determine forecasts for periods 1 01, 102, 103, ... from this model at origin 1 00.

b. What is the shape of the forecast function that evolves from this model?

c. Suppose that the observations for the next four time periods turn out to be 17.5, 21.25, 18.75, and 16.75. Revise your forecasts for periods 102, 103, ... using a rolling horizon approach.

d. If your estimate
 = 0.5, find a 95% prediction interval on the forecast of period 101 made at the end of period 100.