Estimation Methods and Empirics of Hidden Markov Switching Models with Skew-Normal Innovations

We introduce a class of univariate hidden Markov switching models with skew-normal state-dependent innovations, designed to capture regime changes and asymmetric, non-Gaussian features commonly observed in economic and financial time series. Three estimation strategies are developed: (i) exact Maximum Likelihood computed recursively through the Forward (Hamilton) algorithm, (ii) Maximum Likelihood estimation via an EM-type procedure, and (iii) a fast Likelihood-based method relying on linear approximations built from moment-matched Gaussian emissions. Under standard regularity conditions for hidden Markov models and mild additional assumptions for skew-normal distributions, we prove consistency and asymptotic normality of the resulting estimators, enabling reliable large-sample inference. The proposed framework is motivated by an application where switching dynamics and distributional asymmetry are empirically relevant.