Mixture modeling, heavy tailedness, asymmetry and conditional heteroskedasticity in financial returns modelling

Conditional heteroskedasticity models are commonly used for modelling financial time series data which are characterized by extreme and/or skewed observations. These data features might not be properly captured by the most commonly adopted distribution. In this paper, a mixture model for financial time series characterized by conditional heteroskedasticity model is developed, introducing the Finite Mixture of Scale Mixture of Skew Normal of Generalized Autoregressive Conditional Heteroskedastic (FMm-SMSN-GARCH) model. The SMSN distributions allow for the lightly/heavily-tailed, symmetric, and asymmetric distributions providing greater flexibility to handle outliers and complex data. The proposed model has several desirable features, such as the development of a convenient hierarchical representation of the FMm-SMSN family that makes it possible to construct a likelihood function to derive the maximum likelihood estimates via an EM–type algorithm. A comprehensive simulation study and a real-data application demonstrate the superior performance of the proposed method.