A closed-form estimator for the Markov switching in mean model

Abstract

This paper revisits the Markov switching in mean model which is commonly fitted by maximizing its log-likelihood. To effectively resolve the computational complexity caused by the nolinear nature and iterative components in the log-likelihood, we propose a closed-form solution inspired by moment-based and Yule–Walker methods. Associated asymptotics are discussed with numerical evidence. For practical considerations, we demonstrate the usefulness of the proposed estimates when supplied as initial values to obtain the usual maximum likelihood estimates for reliable statistical inferences.