We propose a model for interval-valued time series that specifies the conditional joint distribution of the upper and lower bounds as a mixture of truncated bivariate normal distributions. It preserves the interval natural order and provides great flexibility on capturing potential conditional heteroscedasticity and non-Gaussian features. The standard expectation maximization (EM) algorithm applied to truncated mixtures does not provide a closed-form solution in the M step. A new EM algorithm solves this problem. The model applied to the interval-valued IBM daily stock returns exhibits superior performance over competing models in-sample and out-of-sample evaluation. A trading strategy showcases the usefulness of our approach.

中文翻译：

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区间值时间序列的截断混合转移模型

我们提出了一个区间值时间序列模型，将上限和下限的条件联合分布指定为截断二元正态分布的混合。它保留了区间自然顺序，并为捕获潜在的条件异方差性和非高斯特征提供了极大的灵活性。应用于截断混合物的标准期望最大化 (EM) 算法在 M 步骤中不提供封闭式解。一种新的 EM 算法解决了这个问题。应用于区间值 IBM 每日股票收益的模型在样本内和样本外评估中表现出优于竞争模型的性能。交易策略展示了我们方法的实用性。