Interval‐valued time series has been attracting increasing interest. There have been fruitful results on mean models, but variance models largely remain unexploited. In this article, we propose a conditional heteroskedasticity model for the return interval process, which aims at capturing the underlying variance structure. Under the general framework of random sets, the model properties are investigated. Parameters are estimated by the maximum likelihood method, and the asymptotic properties are established. Empirical application to stocks and financial indices data sets suggests that our model overall outperforms the traditional generalized autoregressive conditional heteroskedasticity for both in‐sample estimation and out‐of‐sample prediction of the volatility.

中文翻译：

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建模返回波动率对波动率预测的方差

间隔值时间序列已引起越来越多的关注。均值模型已经取得了丰硕的成果，但方差模型在很大程度上仍未得到开发。在本文中，我们为收益区间过程提出了一个条件异方差模型，旨在捕获基础方差结构。在随机集的一般框架下，研究模型的属性。通过最大似然法估计参数，并建立渐近性质。对股票和金融指数数据集的经验应用表明，在波动率的样本内估计和样本外预测中，我们的模型总体上优于传统的广义自回归条件异方差。