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 2. Determine forecasts...

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 2. Determine forecasts for periods 101, 102, 103, ... from this model at origin 100.

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

c. Suppose that the observations for the next four time periods turn out to be 53, 55, 46, and 50. Revise your forecasts for periods 102, 103, ... using a rolling horizon approach.

d. If your estimate
 = 1, find a 95% prediction interval on the forecast of period 101 made at the end of period 100.