Markov switching asymmetric GARCH model: stability and forecasting

A new Markov switching asymmetric GARCH model is proposed where each state follows the smooth transition GARCH model, represented by Lubrano (Recherches Economiques de Louvain 67:257–287, 2001), that follows a logistic smooth transition structure between effects of positive and negative shocks. This consideration provides better forecasts than GARCH, Markov switching GARCH and smooth transition GARCH models, in many financial time series. The asymptotic finiteness of the second moment is investigated. The parameters of the model are estimated by applying MCMC methods through Gibbs and griddy Gibbs sampling. Applying the log return of some part of S&P500\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S \& P\ 500$$\end{document} indices, we show the competing performance of in sample fit and out of sample forecast volatility and value at risk of the proposed model. The Diebold–Mariano test shows that the presented model outperforms all competing models in forecast volatility.