Cross-correlation of point series using a new method

Traditional methods of cross-correlation of two time series do not apply to point time series. Here, a new method, devised specifically for point series, utilizes a correlation measure that is based in the rms difference (or, alternatively, the median absolute difference) between nearest neightbors in overlapped segments of the two series. Error estimates for the observed locations of the points, as well as a systematic shift of one series with respect to the other to accommodate a constant, but unknown, lead or lag, are easily incorporated into the analysis using Monte Carlo techniques. A methodological restriction adopted here is that one series be treated as a template series against which the other, called the target series, is cross-correlated. To estimate a significance level for the correlation measure, the adopted alternative (null) hypothesis is that the target series arises from a homogeneous Poisson process. The new method is applied to cross-correlating the times of the greatest geomagnetic storms with the times of maximum in the undecennial solar activity cycle.