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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.

Thanks.

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    AR(1) processes **ARE** Markov chai$n$s. Most Markov chains are not AR(1).2011-11-03

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