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Monitoring Shifts in Mean: Asymptotic Normality of Stopping Times
by
Alexander Aue
Clemson University
Coauthors: Lajos Horváth, University of Utah;
Piotr Kokoszka, Utah State University;
Josef Steinebach, Universität zu Köln
We consider a sequential procedure designed to detect a possible change in the mean of a random sequence. The procedure is motivated by the problem of detecting an early change in the mean of returns and is based on the CUSUM (cumulative sum) statistic. It terminates when the CUSUM crosses a boundary function or the number of collected observations reaches a prescribed number. We show that the stopping time is asymptotically normal. Simulations using models derived from returns on indexes and individual stocks show that the normal approximation holds in finite samples.
Date received: April 19, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cauc-82.