Time series

Question 4 [Total marks=26] Consider the model (1 - 0.43B) (1 - B)X, = d, where a, has zero mean and variance ? = 2. Given the observations X49 = 33.4, and Xso = 33.9, (a) determine the formula that gives the /-step ahead forecasts X, (1). (4) (b) Compute Xso(/) for / = 1, 2, 3. (6) (c) Given that for the Gaussian process, the (1 - a) 100% forecast limits are X, (1 ) + Za/2 1 + 2 43 .. 7=1 where Za is a standard normal deviate such that P (Z > Za ) = ~, find the 95% forecast limits for X,+1 and X,+3- (10) (d) At / = 51, Xsi became known and equaled 34.1. Update the forecasts obtained in part (b). (6)