Sequential Tests and Change Detection in the Covariance Structure of Weakly Stationary Time Series

Abstract

Sequential tests and sequential procedures to detect change in the mean or the covariance structure of a linear process are defined. The new tests fix the probability of Type 1 error, and stop after a maximal sample size is reached. They extend methods defined under more restrictive assumptions.

Keywords:

• Approximations
• Brownian motion
• Change in parameters
• Linear processes

Mathematics Subject Classification:

• Primary 6M10
• Secondary 62L10

Acknowledgments

The authors are greatly indebted to a referee for the careful reading of the manuscript and for the numerous suggestions that improved the presentation of our results. E. Gombay's research is partially supported by NSERC and L. Horváth's research is supported by NSF grant DMS 0604670 and grant RGC-HKUST 6428/06H.