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Scan statistics for detecting a local change in variance for normal data with unknown population variance


  • Zhao, Bo
  • Glaz, Joseph


In this article we investigate the performance of fixed, multiple and variable window scan statistics in detecting a local change in variance for a sequence of normal observations, when the population variance of the underlying normal distribution is unknown. For fixed window scan statistics, we study: the training sample approach, the conditioning on sufficient statistic approach and the parametric bootstrap testing approach. It is evident from the numerical results that the scan statistic constructed via the conditioning approach outperforms the other two fixed window scan statistics investigated in this article. Based on power calculation presented in this article, one can conclude that when the size of the window where a local change of variance has occurred is unknown, multiple and variable window scan statistics outperform fixed window scan statistics. The multiple and variable window scan statistics perform equally well. When the sequence of observations is large, the implementation of the multiple window scan statistic is computationally more practical.

Suggested Citation

  • Zhao, Bo & Glaz, Joseph, 2016. "Scan statistics for detecting a local change in variance for normal data with unknown population variance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 137-145.
  • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:137-145
    DOI: 10.1016/j.spl.2015.12.020

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    References listed on IDEAS

    1. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    2. Loredana Ureche-Rangau & Franck Speeg, 2011. "A simple method for variance shift detection at unknown time points," Economics Bulletin, AccessEcon, vol. 31(3), pages 2204-2218.
    3. Andreu Sansó & Vicent Aragó & Josep Lluís Carrion, 2003. "Testing for Changes in the Unconditional Variance of Financial Time Series," DEA Working Papers 5, Universitat de les Illes Balears, Departament d'Economía Aplicada.
    4. Wang, Xiao & Zhao, Bo & Glaz, Joseph, 2014. "A multiple window scan statistic for time series models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 196-203.
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