Detecting shifts in correlation and variability with application to ENSO-monsoon rainfall relationships

Summary

This paper addresses the retrospective detection of step changes at unknown time points in the correlation structure of two or more climate times series. Both the variance of individual series and the covariance between series are addressed. For a sequence of vector-valued observations with an approximate multivariate normal distribution, the proposed method is a parametric likelihood ratio test of the hypothesis of constant covariance against the hypothesis of at least one shift in covariance. The formulation of the test statistic and its asymptotic distribution are taken from Chen and Gupta (2000). This test is applied to the series comprised of the mean summer NINO3 index and the Indian monsoon rainfall index for the years 1871–2003. The most likely change point year was found to be 1980, with a resulting p-value of 0.12. The same test was applied to the series of NINO3 and Northeast Brazil rainfall observations from the years 1856–2001. A shift was detected in 1982 which is significant at the 1% level. Some or all of this shift in the covariance matrix can be attributed to a change in the variance of the Northeast Brazil rainfall. A variation of this methodology designed to increase power under certain multiple change point alternatives, specificallly when a shift is followed by a reversal, is also presented. Simulations to assess the power of the test under various alternatives are also included, in addition to a review of the literature on alternative methods.