For a bivariate VAR(2) model ???????? = ????1????????−1 + ????2????????−2 + ????????, with

????1 =

[1.5 −0.6 0.3 0.2

]

????2 =

[

−0.5 0.3 0.7 −0.2

]

???? =

[

4 1 1 2]

(a) Verify that this model is stationary based on the nature of the roots of det{???? −

????1???? − ????2????2}=0. (Note that you may want to make use of the result of Exercise 14.3 for computational convenience.)

(b) Calculate forecasts ????̂ ????(????) for ???? = 1, … , 5 steps ahead, given that ???????? =

(1.2, 0.6)′ and ????????−1 = (0.5, 0.9)′

.

(c) Find the coefficient matrices ????????, ???? = 1, … , 4, in the infinite MA representation of the process, and find the forecast error covariance matrices ????(????) for ???? =

1, … , 5.