Parameter Estimation of MSNBurr-Based Hidden Markov Model: A Simulation Study

Hidden Markov Model (HMM) is a well-known probabilistic framework for representing sequential phenomena governed by doubly stochastic processes. Specifically, it features a Markov chain with hidden (unobserved) states, where each state emits observable values through a state-conditioned emission distribution at every time step. In this framework, selecting an appropriate emission distribution is essential because an unsuitable choice may prevent the HMM from accurately representing the observed phenomenon. To accommodate emission phenomena with situational symmetry, we propose an HMM framework with an adaptive emission distribution, named MSNBurr-HMM. This method is based on the MSNBurr distribution, which can effectively represent symmetric, right-skewed, and left-skewed emission patterns. We also provide its parameter estimation algorithm using the Baum–Welch algorithm. For model validation, we conduct fitting simulations across diverse scenarios and compare the findings against Gaussian-HMM and Fernández–Steel Skew Normal-HMM using log-likelihood, the Akaike Information Criterion (AIC), the corrected AIC (AICc), and the Bayesian Information Criterion (BIC). The results demonstrate that the algorithm can effectively estimate the target parameters accurately in all tested scenarios. In terms of performance, MSNBurr-HMM generally outperforms other models with strong dominance in various aspects across all evaluation metrics, confirming the promising and excellent results of this proposed method.