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Detecting serial dependence in tail events: A test dual to BDS test

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  • Diks, C.G.H.

    (Universiteit van Amsterdam)

Abstract

A test for serial independence is proposed which is related to the BDS test but focuses on tail event probabilities rather than probabilities near the center of the distribution. The motivation behind this approach is to make the test more suitable for detecting structure in the tails, such as remaining ARCH- or GARCH-type structure in standardized residuals of financial time series. The new test can be implemented easily by slight modification of the standard BDS test, and is also suitable for model identification. The BDS test and the modified version are compared numerically. To enable fair power comparisons, both tests are implemented as exact level Monte Carlo tests, enabling power calculations of the tests at identical actual sizes. The Monte Carlo implementation allows the use of test statistics which are considerably simpler than for the standard BDS test. For all nonlinear stochastic models examined the power of the new test is found to be uniformly larger over all practically reasonable values of the bandwidth parameter. The test is illustrated with an empirical application.

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  • Diks, C.G.H., 2002. "Detecting serial dependence in tail events: A test dual to BDS test," CeNDEF Working Papers 02-09, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    • Handle: RePEc:ams:ndfwpp:02-09
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    Cited by:

    1. Evzen Kocenda & Lubos Briatka, 2004. "Advancing the iid Test Based on Integration across the Correlation Integral: Ranges, Competition, and Power," CERGE-EI Working Papers wp235, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    2. Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).
    3. Evzen Kocenda & Lubos Briatka, 2005. "Optimal Range for the iid Test Based on Integration Across the Correlation Integral," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 265-296.

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