Consider the IMA(0, 2, 2) process with parameters ????1 = 0.8 and ????2 = −0.4.

(a) Is the process invertible? If so, what is the expected pattern of the ???? weights?

(b) Calculate and plot the first ten ???? weights for the original series ???????? and comment.

(c) Calculate and plot the first ten ???? weights for the differenced series ???????? =

(1 − ????)

2????????.

4.4 Given the following series of random shocks ????????, and given that ????0 = 20, ????−1 = 19, t a???? t a???? t a????

0 −0.3 5 −0.6 10 −0.4 1 0.6 6 1.7 11 0.9 2 0.9 7 −0.9 12 0.0 3 0.2 8 −1.3 13 −1.4 4 0.1 9 −0.6 14 −0.6

(a) Use the difference equation form of the model to obtain ????1, ????2, … , ????14 for each of the five models in Exercise 4.1.

(b) Plot the resulting series.