Monitoring correlation change in a sequence of random variables
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Date
2012-03-29
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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.
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Keywords
correlation changes, Gaussian process, online detection, threshold function