Asymptotically Optimal Methods of Early Change-Point Detection

In this article the problem of early change-point detection is considered. The main difference from traditional sequential change-point detection problems consists in the nature of changes: we consider both gradual and abrupt changes and wish to detect instants of the beginning of these changes as soon as possible on condition that false alarms are few. We prove the theoretical informational inequalities for the main performance characteristics of early change-point detection methods that help us to consider the asymptotically optimal methods. Our criterion of asymptotic optimality does not coincide with traditional criteria of Shiryaev (1963), Lorden (1971), and Pollak (1985) but allows us to consider both univariate and multivariate nonstationary stochastic models. Besides the theoretical analysis of univariate and multivariate models with changes, we present results of the Monte Carlo study of the proposed methods.