SEP-HMM: A Flexible Hidden Markov Model Framework for Asymmetric and Non-Mesokurtic Emission Patterns

This paper proposes a new Hidden Markov Model (HMM) framework integrated with the Skew Exponential Power (SEP) distribution, named SEP-HMM. The primary advantage of this method is its ability to capture and represent asymmetric and non-mesokurtic emission patterns, which are often encountered in real-world phenomena. This advantage makes it more flexible than well-known HMMs, such as Gaussian-HMM, which are still rigidly based on symmetric and mesokurtic assumptions. We formulate and present its complete algorithm for parameter estimation and hidden state decoding. To test its effectiveness, we run simulations with various scenarios and apply SEP-HMM to real datasets consisting of stock price and temperature datasets. In the simulations conducted, the superiority of SEP-HMM compared to Gaussian-HMM and Skew Normal-HMM is confirmed in most of the replications, both in assessing model fit and in identifying hidden states. This is also supported by the real-case dataset, where SEP-HMM outperforms the benchmark models in all tested metrics.