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Monitoring Constancy Of Variance In Conditionally Heteroskedastic Time Series

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  • Horváth, Lajos
  • Kokoszka, Piotr
  • Zhang, Aonan

Abstract

We propose several methods of on-line detection of a change in unconditional variance in a conditionally heteroskedastic time series. We follow the paradigm of Chu, Stinchcombe, and White (1996, Econometrica 64, 1045–1065) in which the first m observations are assumed to follow a stationary process and the monitoring scheme has asymptotically controlled probability of falsely rejecting the null hypothesis of no change. Our theory is applicable to broad classes of GARCH-type time series and relies on a strong invariance principle that holds for the squares of observations generated by such models. Practical implementation of the procedures, which uses a bandwidth selection procedure of Andrews (1991, Econometrica 59, 817–858), is proposed, and the performance of the methods is investigated by a simulation study.This research was partially supported by NSF grants INT-0223262 and DMS-0413653 and NATO grant PST.EAP.CLG 980599.

Suggested Citation

  • Horváth, Lajos & Kokoszka, Piotr & Zhang, Aonan, 2006. "Monitoring Constancy Of Variance In Conditionally Heteroskedastic Time Series," Econometric Theory, Cambridge University Press, vol. 22(3), pages 373-402, June.
    • Handle: RePEc:cup:etheor:v:22:y:2006:i:03:p:373-402_06
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    1. Wang, Xinyu & Qi, Zikang & Huang, Jianglu, 2023. "How do monetary shock, financial crisis, and quotation reform affect the long memory of exchange rate volatility? Evidence from major currencies," Economic Modelling, Elsevier, vol. 120(C).
    2. Hoga, Yannick, 2017. "Monitoring multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 105-121.
    3. Chen, Zhanshou & Tian, Zheng, 2010. "Modified procedures for change point monitoring in linear models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 62-75.
    4. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Testing for a change in persistence in the presence of non-stationary volatility," Journal of Econometrics, Elsevier, vol. 147(1), pages 84-98, November.
    5. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2011. "Analyzing the structural behavior of volatility in the Major European Markets during the Greek crisis," Economics Bulletin, AccessEcon, vol. 31(4), pages 3016-3029.
    6. Andreou, Elena & Ghysels, Eric, 2008. "Quality control for structural credit risk models," Journal of Econometrics, Elsevier, vol. 146(2), pages 364-375, October.
    7. Xu, Ke-Li, 2013. "Powerful tests for structural changes in volatility," Journal of Econometrics, Elsevier, vol. 173(1), pages 126-142.
    8. Hsu, Chih-Chiang, 2007. "The MOSUM of squares test for monitoring variance changes," Finance Research Letters, Elsevier, vol. 4(4), pages 254-260, December.
    9. Luis A. Gil-Alana & Goodness C. Aye & Rangan Gupta, 2012. "Testing for Persistence with Breaks and Outliers in South African House Prices," Working Papers 201233, University of Pretoria, Department of Economics.
    10. Chen, Zhanshou & Xing, Yuhong & Li, Fuxiao, 2016. "Sieve bootstrap monitoring for change from short to long memory," Economics Letters, Elsevier, vol. 140(C), pages 53-56.
    11. Wang, Xinyu & Luo, Yi & Wang, Zhuqing & Xu, Yan & Wu, Congxin, 2021. "The impact of economic policy uncertainty on volatility of China’s financial stocks: An empirical analysis," Finance Research Letters, Elsevier, vol. 39(C).
    12. Robert Akunga & Ahmad Hassan Ahmad & Simeon Coleman, 2023. "Financial market integration in sub‐Saharan Africa: How important is contagion?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(4), pages 3637-3653, October.

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