The following observations represent values ????91, ????92, … , ????100 from a series fitted by the model ∇???????? = ???????? − 1.1????????−1 + 0.28????????−2:

166, 172, 172, 169, 164, 168, 171, 167, 168, 172

(a) Generate the forecasts ????̂100(????) for ???? = 1, 2, … , 12 and draw a graph of the series values and the forecasts (assume ????90 = 0, ????91 = 0).

(b) With ????̂ 2

???? = 1.103, calculate the estimated standard deviations ????̂(????) of the forecast errors and use them to calculate 80% probability limits for the forecasts. Insert these probability limits on the graph, on either side of the forecasts.