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Is there a simple way to approximate a Markov Chain as an Autoregressive Process, for instance, an AR(1) process?

I am aware that it is easy to approximate an AR(1) process with a Markov Chain, but I am not sure about the converse.


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AR(1) processes ARE Markov chains. Most Markov chains are not AR(1). – Did Nov 3 '11 at 20:30

AR(1) processes are Markov chains only if the innovation/error term is independent of the past.

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