A company is modelling its quarterly overseas sales data, Xt, and is working with two alternative forecasting models: Model 1: Model 2: Xt = aXt-1 + Et Xt = u + Bet-1 + Et i.e. i.e. Xt = Ft + Et Xt = Ft + Et where Ft is a model's forecast sales for quarter t, Xt is the actual sales for quarter t, and et is the error term in the model for quarter t. Suppose the company believe the best values for a, and u are 1.05, 0.5 and 140 respectively. Two years of data are given below Quartert 12 3 4 5 6 7 8 Sales Xt | 120.0 130.0 125.0 130.0 140.0 150.0 160.0 | 150.0 (a) Produce the one quarter ahead forecasts provided by each model for quarters 2 through to 9. Using mean absolute error (based upon forecasts for quarters 2 to 8) as a performance measure, which model appears to be the better one? (9 marks) (b) For each model, write down an expression for an N - quarter ahead forecast and use it to make a forecast (made after the data for quarter 8 is known) for sales in quarter 12. (4 marks)