Reaction times of monitoring schemes for ARMA time series
Loading...
Date
2013-12-16
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
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.
Description
Table of contents
Keywords
CUSUM statistic, structural break detection, Page's CUSUM, Online monitoring, One-step ahead predictors