Abstract: With the development of social technology, more and more types of financial time series have been saved, and interval-valued time series is one of them. The existing research shows that the interval-valued time series contains more information than the point-valued time series, and the study of the financial interval-valued time series can provide a theoretical basis for the investment and prediction of the financial market. However, the influence of abnormal interval on interval-valued time series modeling is rarely noticed in the existing research of interval-valued time series. Therefore, this paper studies the IO-type abnormal interval of interval-valued time series and its test method.
Unlike point-valued time series, the numerical level of interval-valued time series is affected by the upper and lower limit series or the center and radius series. Besides, the affections caused by two partitioned subsequences would also be interacted with each other. Because the center and radius sequence can better reflect the change of interval value, this paper analyzes the IO type abnormal interval from the perspective of center and radius sequence. Three forms of IO-type abnormal interval in interval-value time series are given on the basis of traditional definitions of outliers, namely horizontal drift, temporary change and oblique rise. The mathematical expressions of three types of IO-type exception intervals are given to facilitate the subsequent research on the IO-type exception interval of interval-value time series. Then this paper proposes an IO-type anomaly interval detection algorithm for interval-value time series based on hypothesis testing. Using the idea of interval-value time series research based on statistical methods, ARMA modeling is carried out for the two sequences respectively from the interval center sequence and the interval radius sequence, and the corresponding model residual test statistics at each time are further constructed. The test statistics at each time are compared with the critical value to determine the time point of occurrence of the exception interval. This overall test method will cause large errors, so the Bonferroni law is adopted to ensure that the maximum probability of incorrectly identifying IO type anomaly interval is 5%. Finally, for the daily maximum and minimum prices of the Shanghai Composite Index from January 4, 2016 to December 28, 2018 constitutes the interval-value time series, its daily closing price constitutes the point-value time series, and the proposed detection method is used to detect the abnormal interval.
Based on the analysis of the statistical significance and actual performance of the abnormal interval detection results of interval time series, it is concluded that the abnormal interval detected by the method proposed in this paper is effective. At the same time, by comparing the results of interval-value time series anomaly detection and point-valued time series anomaly detection, it is proved that the proposed interval-value time series anomaly detection method based on hypothesis test is more efficient than the point-valued time series anomaly detection method based on hypothesis test. Different types of anomaly interval detection methods are compared.It can be proved that the anomaly interval detection method based on hypothesis test proposed in this paper has more obvious advantages when facing interval-valued data with the same time period.
Consequently, the research of this paper expands the application field of the principle and technology of classical outlier detection. Furthermore, it also enriches the research scope of interval value time series analysis.It can provide reference for the detection of outliers in other types of time series data and further research on prediction theory. The identification and detection of outliers in interval value time series can provide a certain technical guarantee for improving its prediction accuracy.

Key words: interval-valued time series, outliers, IO-type anomaly interval, detection, shanghai composite index

摘要： 针对区间值时间序列的异常点检测问题,从区间数据的区间中心和区间半径出发,基于ARIMA的点值时间序列IO型异常点检测原理,构造一类区间值时间序列IO型异常区间的检测方法。其中,对区间值时间序列IO型异常区间的概念和类型进行了具体的界定,给出了区间值时间序列IO型异常区间的检测步骤。最后,针对上证指数2016年1月4日到2018年12月28日每日最高价和最低价构成区间值时间序列且其每日收盘价构成点值时间序列,用所提方法进行IO型异常区间的检测,通过和传统点值异常检测结果的对比分析表明,所提方法能够更有效地识别出金融时间序列中存在的异常状况。

关键词: 区间值时间序列, 异常点, IO型异常区间, 检测, 上证指数