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Change point detection and estimation methods under gamma series of observations

Abstract

The aim of the article is to analyze inhomogeneous time series data caused by the presence of an unknown change point. We assume that the time series data are from a gamma distribution with an unknown time point of change in the scale and/or shape parameters. A complete change point methodology is proposed including change detection methodology based on the likelihood ratio statistic as well as estimation of the unknown change point by the method of maximum likelihood estimation (mle). Furthermore, we provide asymptotic distribution of the change point mle when a change occurs in the scale parameter of the gamma distribution. Extensive simulations have been conducted to show excellent agreement between the distribution of the change point under finite sample sizes and its asymptotic counterparts. The simulations are conducted under a change in the scale parameter as well as a change in both scale and shape parameters. A comparison analysis between known parameters and estimated parameters indicates that the error committed is negligible. Two examples, one from the financial market and another from climatology, are analyzed to adequately illustrate the proposed inferential methodology.

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Correspondence to Stergios B. Fotopoulos.

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Fotopoulos, S.B., Paparas, A. & Jandhyala, V.K. Change point detection and estimation methods under gamma series of observations. Stat Papers (2021). https://doi.org/10.1007/s00362-021-01248-x

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Keywords

  • Change point detection
  • Change point estimation
  • Two-sided random walk
  • Total variation distance
  • Dow-Jones data
  • Minimum temperature data from Uppsala