A method for the estimation of the significance of cross-correlations in unevenly sampled red-noise time series

摘要

We present a practical implementation of a Monte Carlo method to estimate thesignificance of cross-correlations in unevenly sampled time series of data,whose statistical properties are modeled with a simple power-law power spectraldensity. This implementation builds on published methods, we introduce a numberof improvements in the normalization of the cross-correlation function estimateand a bootstrap method for estimating the significance of thecross-correlations. A closely related matter is the estimation of a model forthe light curves, which is critical for the significance estimates. We presenta graphical and quantitative demonstration that uses simulations to show howcommon it is to get high cross-correlations for unrelated light curves withsteep power spectral densities. This demonstration highlights the dangers ofinterpreting them as signs of a physical connection. We show that by usinginterpolation and the Hanning sampling window function we are able to reducethe effects of red-noise leakage and to recover steep simple power-law powerspectral densities. We also introduce the use of a Neyman construction for theestimation of the errors in the power-law index of the power spectral density.This method provides a consistent way to estimate the significance ofcross-correlations in unevenly sampled time series of data.