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A test for self-exciting clustering mechanism

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  • Fama, Yuchen
  • Pozdnyakov, Vladimir

Abstract

In this paper, we propose a test to distinguish between data with cluster pattern where the variables are dependent in a self-exciting fashion versus independently identically distributed random variables. We also developed asymptotic distribution of the test statistic with closed-form covariance structure. Comparisons with scan statistics are discussed in the context of simulated earthquake data. Applications to two data sets are discussed.

Suggested Citation

  • Fama, Yuchen & Pozdnyakov, Vladimir, 2011. "A test for self-exciting clustering mechanism," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1541-1546, October.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1541-1546
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    References listed on IDEAS

    as
    1. Glaz, Joseph & Zhang, Zhenkui, 2006. "Maximum scan score-type statistics," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1316-1322, July.
    2. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
    3. Yu, Chang & Zelterman, Daniel, 2002. "Sums of dependent Bernoulli random variables and disease clustering," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 363-373, May.
    4. Bowman, Dale, 1999. "A parametric independence test for clustered binary data," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 1-7, January.
    5. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 61-82, Suppl. De.
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