The analysis of change-point data with dependent errors

Abstract

We consider abrupt mean-change models for data with dependent, stationary, errors.No specific distributional assumptions, other than the existence and summability of cumulants, are made.A consistency property of the least squares estimator of the change-point is derived.This leads to the construction of consistent, asymptotically normal and efficient estimators of the error spectral density function and covariances.The application of these results in testing for the existence of a change is discussed.A test for uncorrelatedness of the errors is also given.An application is made to the detection of changes in the period of a variable star.The relationship between cusum charts used in statistics and O-C diagrams used in astronomy is pointed out.

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