Online change detection of linear regression models

Abstract

In this paper, we consider the problem of quickly detecting an abrupt change of linear coefficients in linear regression models. In particular, the observer sequentially observes a sequence of observations {(xn, yn)}∞n=1, which is assumed to obey a linear regression model at each time slot n. Some of the coefficients in the linear model change at a fixed but unknown time t. The post-change linear coefficients are unknown to the observer. The observer aims to design an online algorithm to detect the model change based on his sequential observations. Two performance metrics, namely the worst case detection delay (WADD) and the average run length to false alarm (ARL2FA), are adopted to evaluate the performance of detection algorithms. We design a low complexity algorithm, termed as parallel sum algorithm, for the detection purpose. An asymptotic upper bound on WADD is provided under any given ARL2FA constraint.