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

• Published in: Monthly notices of the Royal Astronomical Society 2014-11, Vol.445 (1), p.437-459
• Main Authors: Max-Moerbeck, W., Richards, J. L., Hovatta, T., Pavlidou, V., Pearson, T. J., Readhead, A. C. S.
• Format: Article
• Language: English
• Subjects: Bootstrap method; Computer simulation; Construction; Density; Estimates; Interpolation; Monte Carlo simulation; Sampling; Spectra; Star & galaxy formation; Time series
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stu1707

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 modelled 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.