GARCH-mixture of stable models for financial data analysis

Generalised autoregressive conditional heteroscedasticity (GARCH) models have proved to be very efficient tools in financial data understanding and prediction. Classical GARCH models assume Gaussian excitations. Such models fall short of modelling efficiently abrupt changes in the data due to the nature of Gaussian distributions. Recently extension to GARCH-stable models have been suggested to model impulsive data but such models despite success in modelling abrupt changes, have the difficulty of modelling multi-modal data. In this work, we discuss a further extension to GARCH-mixture of stable models utilising mixture of stable densities which have been suggested recently in signal processing and statistics literatures independently. We also provide a scheme for the estimation of the parameters of the model based on Markov Chain Monte Carlo. An important difference from previous work on mixture models is that the technique automatically estimates the number of components in the mixture using reversible jump MCMC. We test the method in modelling various financial data and demonstrate the performance improvement over existing models. We believe that GARCH-mixture of stable models provide a very flexible yet economic tool for modelling various types of financial data which posses impulsive, skewed and multimodal characteristics.