Time series clustering based on latent volatility mixture modeling with applications in finance

Modeling financial time series data poses a significant challenge in the realm of time series analysis. The Autoregressive Conditional Heteroskedasticity (ARCH) model stands out as a potent tool for capturing time-varying volatility and heteroskedasticity in financial data. However, conventional ARCH models display sensitivity to departures from normality, leading to the development of extensions employing more flexible distributions. In this context, we propose a robust enhancement to the mixture of ARCH (MoARCH) model by integrating normal mean–variance mixture (NMVM) distributions to model component errors. The stochastic representation of the proposed model allows for a straightforward implementation of an Expectation Conditional Maximization Either (ECME) algorithm for obtaining Maximum Penalized Likelihood estimates (MPL). To thoroughly evaluate the model, we conduct four simulation studies to explore finite-sample properties, assess MPL estimators, scrutinize model robustness, and evaluate the accuracy of our proposal in fitting, clustering, and forecasting. Practical applications further highlight the effectiveness of our methodology, showcasing successful implementations across diverse real datasets.