An estimator of the number of change points based on a weak invariance principle

Abstract

We study an estimator of the number of change points in the drift of a stochastic process based on the Schwarz criterion. In a general statistical model where the additive measurement noise satisfies a certain weak invariance principle (examples included are partial sums, renewal processes, and linear processes in time series analysis) consistency can be shown under the condition that the number of jumps is not greater than a given upper bound.