AD model

Min Kim (min.kim@rutgers.edu)

yt=ϕEtyt+1+ϕutut=ρut1+et

which can be rewritten as

[ut+1Eyt+1]=F[utyt]+G[et+10]

where F=[ρ011/ϕ] and G=[1000].

Recall that we have one forward-looking variable, that is, y. Hence, in order to satisfy BK condition, we need one eigen value outside of unit circle in matrix F.

12.8 μs
139 s
200 ns
11.3 μs

BK is satisfied?

8.8 μs

Yes!

45.1 μs

Let's check the decomposition as well

8.1 μs
Λ
2×2 Matrix{Float64}:
 0.5  0.0
 0.0  1.5
12.3 μs
D
2×2 Matrix{Float64}:
 0.707107  0.0
 0.707107  1.0
49.6 μs
true
8.8 μs