Use of cross correlations in the search for teleconnections

The search for teleconnections usually involves the calculation of sample cross correlation functions for pairs of atmospheric/oceanic time series. Properties of the theoretical cross correlation function are derived by means of analytical techniques, and properties of the sample cross correlation function are obtained by means of simulations. In particular, the effect of autocorrelation of the individual time series is to ‘smear out’ any contemporaneous cross correlation that might be present, producing nonzero cross correlations at nonzero lags. To combat this problem, the advantages of ‘prewhitening’ before computing cross correlations are demonstrated. Moreover, the operation of smoothing individual time series has the effect of inflating the values of the cross correlation coefficients at nonzero lags. Finally, the behaviour of running cross correlation coefficients is somewhat counterintuitive, making this technique potentially very misleading for detecting changes in relationships over time. For illustrative purposes, these calculations are also performed for Darwin and Tahiti time series of monthly sea level pressure.