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

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

Suppose {*Y _{t}*} is the AR(1) process

*Y _{t}*=

*φY*

_{t}_{−1}+

*Z*

_{t},where {*Z _{t}*} is an iid sequence of random variables with mean 0 and some probability

density function *f(x)*. Then with *X _{t}*:=

*Y*

_{t}_{−1}we have

*p(y _{t}*|

*x*=

_{t})*f (y*−

_{t}*φx*

_{t})and