Consider the K-dimensional Gaussian stable VAR(1) process yt = Ayt1 +ut with y0 N(0, 0) and ut N(0,u) for t = 1, 2,

Consider the K-dimensional Gaussian stable VAR(1) process yt = Ayt−1 +ut with y0 ∼ N(0, 0) and ut ∼ N(0,Σu) for t = 1, 2, . . .. Use the Kalman filter recursions to determine yt|t−1.

(a) Show that yt|t−1 = Ayt−1.

(b) Show that the conditions of Proposition 18.1 are satisfied if

δ = 
vec(A)
vech(Σu)

.