Open Access
May 2015 Reaction times of monitoring schemes for ARMA time series
Alexander Aue, Christopher Dienes, Stefan Fremdt, Josef Steinebach
Bernoulli 21(2): 1238-1259 (May 2015). DOI: 10.3150/14-BEJ604


This paper is concerned with deriving the limit distributions of stopping times devised to sequentially uncover structural breaks in the parameters of an autoregressive moving average, ARMA, time series. The stopping rules are defined as the first time lag for which detectors, based on CUSUMs and Page’s CUSUMs for residuals, exceed the value of a prescribed threshold function. It is shown that the limit distributions crucially depend on a drift term induced by the underlying ARMA parameters. The precise form of the asymptotic is determined by an interplay between the location of the break point and the size of the change implied by the drift. The theoretical results are accompanied by a simulation study and applications to electroencephalography, EEG, and IBM data. The empirical results indicate a satisfactory behavior in finite samples.


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Alexander Aue. Christopher Dienes. Stefan Fremdt. Josef Steinebach. "Reaction times of monitoring schemes for ARMA time series." Bernoulli 21 (2) 1238 - 1259, May 2015.


Published: May 2015
First available in Project Euclid: 21 April 2015

zbMATH: 06445974
MathSciNet: MR3338663
Digital Object Identifier: 10.3150/14-BEJ604

Keywords: CUSUM statistic , on-line monitoring , Page’s CUSUM , structural break detection

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 2 • May 2015
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