Modeling Financial return with Markov Time-Varying Mixed Normal GARCH Model

In previous studies, the normal mixture, as well as the Markov process, were used to model the financial return, separately. In this study, the normal mixture model is extended to the Markov mixture of normals. The mixture weights in every state are considered time-varying and as a function of past observations, so the limit of constant weight assumption is removed. The proposed model is estimated using Bayesian inference and a Gibbs sampling algorithm has been created to compute posterior density. The performance of algorithm is tested with simulation, then a two-state Markov time-varying Mixed Normal-GARCH model (MMN) with one and two components in every state, as well as limited cases (mean zero), were compared by comparison of their likelihood function. Finally, the model is applied to S&P500 and TEPIX daily return and results show that MMN models with two components provide better results than MMN model with one component which is so-called Markov switching GARCH model.