Let { Y t } be the causal AR(1) process given by Y t = φY t −1 + Z t , { Z t } ∼ WN(0 ,σ 2 ) . In…

An AR(1) process

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Let { Y t } be the causal AR(1) process given by Y t = φY t −1 + Z t , { Z t } ∼ WN(0 ,σ 2 ) . In…
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Let {Yt} be the causal AR(1) process given by

YtφYt−1 + Zt , {Zt} ∼ WN(02).

In this case, a state-space representation for {Yt} is easy to construct. We can, for example, define a sequence of state variables Xt by

Xt+1 = φXt Vt, t= 12, . . . ,

where X1 = Y1 =

 width= and VtZt+1. The process {Yt} then satisfies the

observation equation YtXt ,

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