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 ((Formula presented.)) 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 (Formula presented.) 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.