  We study online changepoint detection in the context of a linear regression
model. We propose a class of heavily weighted statistics based on the CUSUM
process of the regression residuals, which are specifically designed to ensure
timely detection of breaks occurring early on during the monitoring horizon. We
subsequently propose a class of composite statistics, constructed using
different weighing schemes; the decision rule to mark a changepoint is based on
the largest statistic across the various weights, thus effectively working like
a veto-based voting mechanism, which ensures fast detection irrespective of the
location of the changepoint. Our theory is derived under a very general form of
weak dependence, thus being able to apply our tests to virtually all time
series encountered in economics, medicine, and other applied sciences. Monte
Carlo simulations show that our methodologies are able to control the
procedure-wise Type I Error, and have short detection delays in the presence of
breaks.
