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Bootstrap tests for structural change with infinite variance observations

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  • Jin, Hao
  • Tian, Zheng
  • Qin, Ruibing
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    Abstract

    The quest of structural change with infinite variance observations appears to be relatively common. Conventional residual CUSUM of squares test (RCUSQ) are unreliable in the presence of such behavior, having nonpivotal asymptotic null distributions. In this paper we propose a residual-based bootstrap approach to RCUSQ testing that is valid against a range of infinite variance processes. Our proposed method does not require the practitioners to specify knowledge for tailed index. Consistency and the rate of convergence for the estimated change point are also obtained. We also show via simulations that our asymptotic results provide good approximations in finite samples. In addition, we apply our results to investigate the original returns for NO.1 SDS using a historical data set that covers the period 1999-2002.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 79 (2009)
    Issue (Month): 19 (October)
    Pages: 1985-1995

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    Handle: RePEc:eee:stapro:v:79:y:2009:i:19:p:1985-1995

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    1. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    2. Piotr Kokoszka & Michael Wolf, 2004. "Subsampling the mean of heavy-tailed dependent observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 217-234, 03.
    3. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
    4. Ibragimov, Rustam, 2008. "Heavy-tailedness and Threshold Sex Determination," Scholarly Articles 2623659, Harvard University Department of Economics.
    5. Horváth, Lajos & Kokoszka, Piotr, 2003. "A bootstrap approximation to a unit root test statistic for heavy-tailed observations," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 163-173, April.
    6. Su, Liangjun & Xiao, Zhijie, 2008. "Testing for parameter stability in quantile regression models," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2768-2775, November.
    7. Ibragimov, Rustam, 2008. "Heavy-tailedness and threshold sex determination," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2804-2810, November.
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    Cited by:
    1. Jin, Hao & Zhang, Jinsuo & Zhang, Si & Yu, Cong, 2013. "The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 25-40.
    2. Jin, Hao & Zhang, Jinsuo, 2011. "Modified tests for variance changes in autoregressive regression," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1099-1109.
    3. Jin, Hao & Zhang, Jinsuo, 2010. "Subsampling tests for variance changes in the presence of autoregressive parameter shifts," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2255-2265, November.

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