Monitoring correlation change in a sequence of random variables Articles uri icon

publication date

  • January 2013

start page

  • 186

end page

  • 196

issue

  • 1

volume

  • 143

international standard serial number (ISSN)

  • 0378-3758

electronic international standard serial number (EISSN)

  • 1873-1171

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.

keywords

  • correlation changes; gaussian process; online detection; threshold function