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 $$ S \& P\ 500$$ S & P 500 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.

中文翻译：

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马尔可夫切换非对称 GARCH 模型：稳定性和预测

提出了一种新的马尔可夫转换非对称 GARCH 模型，其中每个状态都遵循平滑过渡 GARCH 模型，以 Lubrano 为代表（Recherches Economiques de Louvain 67:257–287, 2001），它遵循正冲击和负冲击效应之间的逻辑平滑过渡结构. 在许多金融时间序列中，这种考虑提供了比 GARCH、马尔可夫转换 GARCH 和平滑过渡 GARCH 模型更好的预测。研究了二阶矩的渐近有限性。模型的参数是通过应用 MCMC 方法通过 Gibbs 和 griddy Gibbs 采样来估计的。应用 $$ S \& P\ 500$$ S & P 500 指数的某些部分的对数回报，我们展示了样本拟合和样本外预测波动率和所提出模型的风险价值的竞争表现。