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

TL;DR

This paper introduces an improved Monte Carlo method for assessing the significance of cross-correlations in unevenly sampled red-noise time series, addressing challenges like red-noise leakage and model estimation.

Contribution

It presents novel normalization, bootstrap significance estimation, and error analysis techniques for cross-correlation in unevenly sampled data with red noise.

Findings

High cross-correlations can occur in unrelated light curves with steep power spectra.

Interpolation and Hanning window reduce red-noise leakage effects.

The method reliably estimates significance and errors in power spectral density indices.

Abstract

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