We consider the nonparametric inference for the double-threshold generalized autoregressive conditional heteroscedastic models. The quasi-maximum exponential likelihood estimators (QMELEs) of the model parameters are obtained, and their asymptotic properties are established. Simulation studies imply that the estimators are asymptotically normally distributed. An empirical investigation of stock returns illustrates our findings. Both the simulations and the example indicate that the QMELE is feasible, reliable and appropriate to fit the financial time series data of the Hang Seng Index.

中文翻译：

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双阈值 GARCH 模型的准最大指数似然估计

我们考虑双阈值广义自回归条件异方差模型的非参数推断。获得了模型参数的准最大指数似然估计量（QMELEs），并建立了它们的渐近性质。模拟研究表明估计量是渐近正态分布的。对股票收益的实证调查说明了我们的发现。模拟和示例均表明 QMELE 是可行、可靠且适合拟合恒生指数金融时间序列数据的。