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Abstract
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Time series are often affected by change-points (structural breaks) making the statistical analysis a delicate issue.
Since in real applications data are often data streams where observations arrive sequentially, sequential monitoring procedures, also called surveillance or detection procedures, provide useful tools which signal when there is evidence that a change has occurred.
In this talk, we study some recent procedures and their asymptotics with a focus on problems related to integrated processes. We study detectors based on local linear estimation to monitor the mean as well as methods to detect changes from I(1) to I(0) which can also be applied to detect cointegration. Our asymptotic results deal with functional central limit theorems for the underlying processes, which yield central limit theorems for the related stopping times defining the detectors.
Lastly, we discuss some results on limit theorems for functional(cadlag) data.
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