An AR(1) processAn AR(1) process with iid noise can be expressed as an observation driven model.

An AR(1) process

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An AR(1) process with iid noise can be expressed as an observation driven model.

Suppose {Yt} is the AR(1) process

YtφYt−1 + Zt ,

where {Zt} is an iid sequence of random variables with mean 0 and some probability

density function f(x). Then with Xt:= Yt−1 we have

p(yt|xt ) f (yt− φxt )

and

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