Theoretical and Applied Climatology

, Volume 94, Issue 3–4, pp 215–224

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



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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bollerslev, T 1986Generalized autoregressive conditional heteroscedasticityJ Econometrics31307327CrossRefGoogle Scholar
  2. Chen, J, Gupta, AK 2000Parametric statistical changepoint analysisBirkhäuser PressBostonGoogle Scholar
  3. Chiang, J, Kushnir, Y, Zebiak, S 2000Interdecadal changes in eastern Pacfic ITCZ variability and its influence on the Atlantic ITCZGeophys Res Lett2736873690CrossRefGoogle Scholar
  4. Gershunov, A, Schneider, N, Barnett, T 2001Low-frequency modulation of the ENSO-Indian monsoon rainfall relationship: signal or noise?J Climate1424862492CrossRefGoogle Scholar
  5. Giacomini E, Hardle WK, Ignatieva E, Spokoiny V (2006) Inhomogeneous dependency modeling with time varying copulaeling with time varying copulae. SFB 649 Discussion Papers Humboldt University, Berlin, GermanyGoogle Scholar
  6. Krishnamurthy, V, Boswani, BN 2000Indian Monsoon-ENSO relationship on interdecadal timescaleJ Climate13570595Google Scholar
  7. Kumar, KK, Rajagopalan, B, Cane, M 1999On the weakening relationship between the Indian monsoon and ENSOScience28421562159CrossRefGoogle Scholar
  8. Lehmann, EL 2000Testing statistical hypothesesSpringerNew YorkGoogle Scholar
  9. Maraun, D, Kurths, J 2005Epochs of phase coherence between El Nino/Southern Oscillation and Indian MonsoonGeophys Res Lett32L15709CrossRefGoogle Scholar
  10. Mercurio, D, Spokoiny, V 2004Statistical inference for time-inhomogeneous volatility modelsAnn Stat32577602CrossRefGoogle Scholar
  11. Parthasarathy, B, Kumar, KR, Munot, AA 1991Evidence of secular variations in Indian monsoon rainfall-circulation relationshipsJ Climate4927938CrossRefGoogle Scholar
  12. Sveinsson, OGB, Salas, JD, Boes, DC, Pielke, RA 2003Modeling the dynamics of long-term variability of hydroclimatic processesJ Hydrometeorol4489506CrossRefGoogle Scholar
  13. Yeh, A, Lin, D, McGrath, R 2006Multivariate control charts for monitoring covariance matrix: a reviewQuality Technology Quantitative Management3415436Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Lamont-Doherty Earth Observatory of Columbia UniversityPalisadesUSA

Personalised recommendations