Markov Chains as Autoregressive Processes

Question

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.

Answer 1

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