This study considers interval-valued time series data. To characterize such data, we propose an auto-interval-regressive (AIR) model using the order statistics from normal distributions. Furthermore, to better capture the heteroscedasticity in volatility, we design a heteroscedastic volatility AIR (HVAIR) model. We derive the likelihood functions of the AIR and HVAIR models to obtain the maximum likelihood estimator. Monte Carlo simulations are then conducted to evaluate our methods of estimation and confirm their validity. A real data example from the S&P 500 Index is used to demonstrate our method.

中文翻译：

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基于自动间隔回归模型的时间序列符号间隔值数据分析

本研究考虑区间值时间序列数据。为了表征此类数据，我们使用正态分布的阶次统计量提出了一个自动间隔回归（AIR）模型。此外，为了更好地捕捉波动率的异方差，我们设计了异方差波动率AIR（HVAIR）模型。我们导出AIR和HVAIR模型的似然函数，以获得最大似然估计量。然后进行蒙特卡洛模拟，以评估我们的估计方法并确认其有效性。标准普尔500指数的真实数据示例用于说明我们的方法。