EWMA Charts for Detecting a Change-Point in the Drift of a Stochastic Process

Abstract

In an earlier paper, we suggested and analyzed some new (truncated) stopping rules for detecting a change-point in the drift of a renewal counting process under the assumption that information on the process under observation only was available at discrete equidistant timepoints, by embedding the observed process into a Gaussian framework. The present paper is devoted to the investigation of analogous stopping rules related to EWMA (exponentially weighted moving average) charts, which allow for a more flexible change detection procedure.

Key Words:

• EWMA chart
• Change-point
• Renewal counting process
• Increment
• Strong approximation
• Wiener process
• Stationary process
• Extreme value asymptotics

AMS 2000 Subject Classifications:

• Primary 62G10, 62G20, 62G32, 62L10
• Secondary 60F17, 60G40, 60G70, 60J65, 60K05

Acknowledgments

This work began during the first author's visit in Köln. He wishes to thank his coauthor and the Institute of Mathematics there for their hospitality and support. He also wishes to thank Kungliga Vetenskapssamhället i Uppsala for the travel grant.

Notes

Recommended by A. Martinsek