ARTICLE

Volume 2,Issue 7

Cite this article
7
Download
22
Citations
159
Views
20 April 2026

GARCH 型过程稳健控制设计及其在金融市场监控中的应用

志坚 王1 智 麦1
Show Less
1 广东财经大学统计与数据科学学院, 中国
ASDS 2026 , 2(4), 49–55; https://doi.org/10.61369/ASDS.2026040010
© 2026 by the Author(s). Licensee Art and Technology, USA. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC BY-NC 4.0) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

传统GARCH 型质量控制图的中心限与控制上下限对离群值敏感,常会导致监测结果与实际不符。本研究采用HLShamos稳健组合估计量与Huber 权函数对其进行稳健改进,构建出稳健GARCH 型控制图。数值模拟结果发现:第一,在不同样本量、不同污染率下,稳健GARCH 型控制图与删除离群值的传统控制图监测效果接近,而与含离群值的传统控制图相差较大。第二,随着污染率增加,传统控制图异方差控制限间距逐渐增大,而稳健控制图几乎不变或变化轻微。第三,在大样本、高污染率下,传统控制图异方差控制限近似成直线型且远离控制中心限,而稳健控制图却改变不大,表现出较强的抗差性和稳健性。实证分析结果进一步验证了稳健GARCH 型控制图的可行性和有效性。研究结论可用于离群值与异方差并存的时间序列稳健建模及统计过程控制。

Keywords
GARCH 型控制图
HL-Shamos 组合估计量
Huber 权函数
稳健估计
References

[1]Ajadi JO, Zwetsloot IM, Tsui K-L. A New Robust Multivariate EWMA Dispersion Control Chart for Individual Observations[J]. Mathematics. 2021,9(9) :1-18.
[2]Koyuncu, N., Karagöz, D. Designing robust modified R control charts for asymmetric distributions under ranked set and median ranked set sampling[J]. Computational Statistics, 2021,36:1093–1121.
[3]Cabana Elisa,Lillo Rosa E.. Robust multivariate control chart based on shrinkage for individual observations[J]. Journal of Quality Technology,2022,54(4):415-440.
[4] Yadpirun Supharakonsakun; Yupaporn Areepong; Korakoch Silpakob.Explicit ARL Computational for a Modified EWMA Control Chart in Autocorrelated Statistical Process
Control Models [J] Computer Modeling in Engineering & Sciences.2025. 145(1): 699-720 .
[5] 张力健, 杨继平, 张秋菊.AR-GARCH 型残差控制图及其应用研究[J]. 中国管理科学,2006, 14(1):15-19.
[6]Sermad Abbas ;Roland Fried. Robust control charts for the mean of a locally linear time series[J], Journal of Statistical Computation and Simulation,2020,90(15):1-25.
[7]Salah Mohamed,Engy Mohamed,Shereen Abdel Latif. Profile monitoring of residuals control charts under gamma regression model[J]. Eastern-European Journal of Enterprise Technologies,2022,6(4):23-31.
[8] Li Xue; Qiuyu Wang; Congkai Li; Lisheng An.Economic design of residuals MEWMA control chart with variable sampling intervals and sample size [J] Communications in Statistics - Simulation and Computation. 2025.54(2) : 467-488.
[9] Ramy M. Khalifa; Soumaya Yacout; Samuel Bassetto; Yasser Shaban.Condition monitoring and warning of a belt drive system based on a logical analysis of data regressionbased residual control chart [J] Structural Health Monitoring. 2025. 24(3): 1657-1673.
[10]Lin Y C, Chao Y C, Chen C H. Robustness of the EWMA median control chart to non-normality[J]. International Journal of Industrial & Systems Engineering, 2017, 25(1):35-45.
[11]Derya Karagöz. Asymmetric control limits for range chart with simple robust estimator under the non-normal distributed process[J].Mathematical Sciences, 2018,12(4) :249-262.
[12]Ishaq Adeyanju Raji,Muhammad Riaz,Nasir Abbas. Robust dual-CUSUM control charts for contaminated processes[J]. Communications in Statistics-Simulation and Computation,2019,48(7):2177-2190.
[13]Liang,Xiang,Pu,Li,Jin. A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions[J]. Quality Technology & Quantitative Management,2019,16(1):113-127.
[14]Nasir Abbas. A robust S2 control chart with Tukey’s and MAD outlier detectors[J].Quality and Reliability Engineering International,2020,36(1):403-413.
[15]Kao Shih Chou. A robust standard deviation control chart based on square A estimator[J]. Quality and Reliability Engineering International,2022,38(5):2715-2730.
[16]Muhammad Arslan; Usman Shahzad; Ali Yeganeh; Huiming Zhu; JC Malela Majika; Shakeel Ahmad.A Robust L ‐Comoments Covariance Matrix ‐Based Hotelling’s T2${T^{2}}$ Control Chart for Monitoring High ‐Dimensional Non ‐Normal Multivariate Data in the Presence of Outliers [J] Quality and Reliability Engineering International. 2025, 41(7): 3308-3317.
[17] Severin T., Schmid W.. Monitoring changes in GARCH models[J]. Allgemeines Statisches Archiv, 1999,83 :281-307.
[18] Schipper S.,Schmid W.. Control charts for GARCH process[J]. Nonlinear Analysis,2001,47:2049-2060.
[19] 夏远强,韩文秀,何民.GARCH 型相关过程及其质量控制图. 天津大学学报[J]. 2003,36(l):92-95.
[20]Sabahno Hamed,Celano Giovanni. Monitoring the multivariate coefficient of variation in presence of autocorrelation with variable parameters control charts[J]. Quality Technology & Quantitative Management,2023,20(2):184-210.
[21] 王志坚. 稳健残差控制图的构建及在金融时序中的应用[J]. 数理统计与管理,2017,36(05):930-942.
[22] 庄芳, 郁淼淼, 吴纯杰. 带参数估计的EWMA 方差控制图稳健性分析[J]. 系统科学与数学,2018,38(01):101-118.
[23] 苏拥英, 王志坚. 常规过程控制图的敏感性分析及稳健设计[J]. 统计与决策,2021,37(10):160-164.
[24]Salih O. Duffuaa, Ahmed M. Ghaithan, Ahmed M. Attia. A mathematical model for the optimal robust design of cause selecting control charts[J]. European Journal of Industrial Engineering, 2022,16(2):169-193.
[25] Atef F. Hashem; Najam ul Hassan; Maqbool Hussain Sial; Syed Muhammad Muslim Raza.A novel coefficient of variation based distance weighted control chart for the monitoring of nuclear event data [J] Journal of Radiation Research and Applied Sciences..2025,18(3) :101743-10174.
[26] Chanseok Park, Haewon Kim & Min Wang . Investigation of finite-sample properties of robust location and scale estimators[J].Communications in Statistics - Simulation and Computation, 2022,51(5):2619-2645.
[27] 王志坚, 王斌会. 稳健改进的AO 型异常点检测法在金融时序中的应用[J]. 数理统计与管理. 2016, 35(2):369-380.

Share
Back to top