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This paper aims to analyse epidemic shifts in the mean of a time series. Here, an epidemic refers to a contiguous segment of observations within the sample where the mean shift occurs. The limiting law of our test statistic is obtained by a novel almost sure approximation for \(\alpha \) -mixing processes. The precision of the remainder term in our approximation ensures that our test remains consistent even when the epidemic’s duration scales logarithmically with the sample size.

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On Epidemic Change Point Detection Under Strong Mixing Conditions

  • 章节

  • 发表日期：

    2026年

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  • István Berkes,
  • Siegfried Hörmann

摘要

This paper aims to analyse epidemic shifts in the mean of a time series. Here, an epidemic refers to a contiguous segment of observations within the sample where the mean shift occurs. The limiting law of our test statistic is obtained by a novel almost sure approximation for \(\alpha \) -mixing processes. The precision of the remainder term in our approximation ensures that our test remains consistent even when the epidemic’s duration scales logarithmically with the sample size.