Extending finite mixture models with skew-normal distributions and hidden Markov models for time series

Abstract: We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according to hidden states, the proposed model effectively captures dynamic dependencies between variables. Through the estimation of state-specific parameters, including location, scale, and skewness, the proposed model enables the detection of structural changes, such as shifts in the observed data distribution, while addressing challenges such as overfitting and computational inefficiencies inherent in Gaussian mixtures. Both simulation studies and real data analysis demonstrate the robustness and flexibility of the approach, highlighting its ability to accurately model asymmetric data and detect regime transitions. This methodological advancement broadens the applicability of a finite mixture of hidden Markov models across various fields, including demography, economics, finance, and environmental studies, offering a powerful tool for understanding complex temporal dynamics.