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

作者：Max Moerbeck W^*; Richards J L; Hovatta T; Pavlidou V; Pearson T J; Readhead A C S

来源：Monthly Notices of the Royal Astronomical Society, 2014, 445(1): 437-459.

DOI：10.1093/mnras/stu1707

• methods: data analysis
• methods: statistical
• techniques: miscellaneous

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.

• 出版日期2014-11-21