HYGARCH process is commonly used for modeling long memory volatility. Many financial time series are characterized by transition between different levels of volatilities. Smooth transition HYGARCH (ST-HYGARCH) model is proposed to model smooth transition between components of HYGARCH process. The behavior of the conditional variance in the ST-HYGARCH are allowed to change smoothly over time. The asymptotic finiteness of the second moment is studied. A score test is developed to check the smooth transition property. The performance of the new proposed model and the score test are examined by some simulations. Applying the log returns of some part of S&P500 and Dow Jones industrial average indexes, we show the competing performance of the ST-HYGARCH model in comparison to HYGARCH and ST-GARCH models in forecasting volatility and value-at-risk.

中文翻译：

---

平滑过渡 HYGARCH 模型：稳定性和测试

HYGARCH 过程通常用于对长期记忆波动进行建模。许多金融时间序列的特点是不同波动水平之间的过渡。提出了平滑过渡HYGARCH（ST-HYGARCH）模型来模拟HYGARCH过程各分量之间的平滑过渡。ST-HYGARCH 中条件方差的行为可以随时间平滑变化。研究了二阶矩的渐近有限性。开发了一个分数测试来检查平滑过渡属性。新提出的模型的性能和分数测试通过一些模拟来检验。应用 S&P500 和道琼斯工业平均指数的某些部分的对数回报，我们展示了与 HYGARCH 和 ST-GARCH 模型相比，ST-HYGARCH 模型在预测波动性和风险价值方面的竞争性能。