Confidence curves for change points in hydrometeorological time series

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Abstract

In this paper, a method based on Approximate Empirical likelihood ratio and a Deviance function combined with bootstrapping (AED-BP) is proposed to construct a confidence curve for the location of a change point. The method is compared with a method based on parametric Profile Likelihood and a Deviance function combined with Monte Carlo simulation (PLD-MC). A confidence curve provides a representation of the uncertainty in the outcome of the change point analysis. To evaluate the practical usability of confidence curves constructed by AED-BP, its properties were examined and its performance was compared to that of PLD-MC. The methods were applied to both synthetic and real data. Synthetic data were generated from three parametric distributions: Fréchet with a constant shape parameter, log-normal, and gamma distributions. The real data are the hydrometeorological data analysed in other studies. The change points found in the original publications are used as a reference in this present paper. The results show that AED-BP has a performance that is similar to PLD-MC, but has an advantage in that it is not necessary to select a distribution family for the data. The AED-BP results on the Annual Maximum Runoff series for the stations Yichang and Hankou along the Yangtze river are among the first that show a possible effect of the presence of the Three Gorges dam.
Original languageEnglish
Article number125503
Pages (from-to)1-19
Number of pages19
JournalJournal of Hydrology
Volume590
DOIs
Publication statusPublished - 2020

Keywords

  • Approximate empirical likelihood ratio
  • Change point detection
  • Confidence curves
  • Confidence sets
  • Parametric likelihood ratio
  • Similarity index

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