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A comparison of single and multiple changepoint techniques for time series data

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  • Shi, Xuesheng
  • Gallagher, Colin
  • Lund, Robert
  • Killick, Rebecca

Abstract

Correlated time series data arise in many applications. This paper describes and compares several prominent single and multiple changepoint techniques for correlated time series. In the single changepoint problem, various cumulative sum (CUSUM) and likelihood ratio statistics, along with boundary cropping scenarios and scaling methods (e.g., scaling to an extreme value or Brownian Bridge limit) are compared. A recently developed test based on summing squared CUSUM statistics over all time indices is shown to have controlled Type I error and superior detection power. In the multiple changepoint setting, penalized likelihoods drive the discourse, with AIC, BIC, mBIC, and MDL penalties being considered. Binary and wild binary segmentation techniques are also compared. A new distance metric is introduced that measures differences between two multiple changepoint segmentations. Algorithmic and computational concerns are discussed and simulations are given to support all conclusions. In the end, the multiple changepoint setting admits no clear methodological winner, performance depending on the particular scenario. Nonetheless, some practical guidance emerges.

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  • Shi, Xuesheng & Gallagher, Colin & Lund, Robert & Killick, Rebecca, 2022. "A comparison of single and multiple changepoint techniques for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:csdana:v:170:y:2022:i:c:s0167947322000135
    DOI: 10.1016/j.csda.2022.107433
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