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This paper considers the auto-covariance function (ACVF) of a regime switching AR(1) process. Two independent Markov chains governs on auto-regressive coefficient and standard deviation of white noise process. Our approach to solve this problem is to obtain the ACVF of a AR(1) model with time varying parameters and then extend this result to regime switching case. Finally, an application of our formulae in model selection is proposed.

On ACVF of a regime switching AR(1) process