异方差序列下持久性变点的稳健检验

doi:10.6040/j.issn.1671-9352.0.2025.133

摘要/Abstract

摘要： 在强混合异方差序列的持久性变点检验中,为克服异方差性所导致的最小二乘估计偏差,提出基于最小绝对偏差(least absolute deviation, LAD)估计的比值型检验统计量。在理论上不仅可以避免对长期方差的一致估计,也无须对方差函数进行假设和估计。在一定假设条件下,推导出统计量在原假设下的极限分布,并证明其在备择假设下的一致性。数值模拟结果表明,基于LAD估计的比值型检验具有良好的经验水平,且与最小二乘估计相比,其经验势也表现出较强的稳健性。最后通过一组股价数据,进一步验证本文所提方法的有效性和可行性。

关键词: 持久性变点, 异方差序列, 比值型检验, 最小绝对偏差估计

Abstract: In persistence change-point testing for strongly mixing heteroscedastic sequences, a ratio-based test statistic using least absolute deviation(LAD)estimation is proposed to address the bias in least squares estimation caused by heteroscedasticity. Theoretically, this approach not only avoids the necessity for consistent estimation of long-term variance but also eliminates the need for assumptions or estimation of the variance function. Under some certain conditions, the limit distribution of the statistic under the null hypothesis is derived, and its consistency is proven under the alternative. Numerical simulation indicates that the Ratio-type test based on LAD estimation exhibits good empirical size, and the empirical power also demonstrates satisfactory robustness compared with the least squares estimation. Finally, a set of stock price data are used to further validate the effectiveness and feasibility of the proposed method.

Key words: persistence change, heteroscedastic sequence, ratio-type test, least absolute deviation estimation

中图分类号:

O211

宋家乐,金浩,杨云锋. 异方差序列下持久性变点的稳健检验[J]. 《山东大学学报(理学版)》, 2026, 61(9): 108-122.

SONG Jiale, JIN Hao, YANG Yunfeng. Robust detection of persistence change point in heteroscedastic sequences[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(9): 108-122.

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