Let { Yt } be the MA(1) process Y t = Z t + θZ t −1 , { Z t } ∼ WN(0 ,σ 2 ) . Show that { Yt } has the state-space representation Y t = [1 0] X t , where { X t } is the unique stationary solution of...

Let {Yt} be the MA(1) process

Y_t
=Z_t
+θZ<sub>t

−1</sub>
,{Z_t
} ∼ WN(0,σ
²).

Show that {Yt} has the state-space representation

Y_t
= [1 0]X

_t

 ,

where {X

_t
} is the unique stationary solution of

In particular, show that the state vectorX

_t
can written as