Monitoring correlation change in a sequence of random variables

Abstract

We propose a monitoring procedure to test for the constancy of the correlation coefficient of a sequence of random variables. The idea of the method is that a historical sample is available and the goal is to monitor for changes in the correlation as new data become available. We introduce a detector which is based on the first hitting time of a CUSUM-type statistic over a suitably constructed threshold function. We derive the asymptotic distribution of the detector and show that the procedure detects a change with probability approaching unity as the length of the historical period increases. The method is illustrated by Monte Carlo experiments and the analysis of a real application with the log-returns of the Standard & Poor's 500 (S&P 500) and IBM stock assets.