A method for the estimation of the significance of cross-correlations in unevenly sampled red-noise time series
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.
Additional Information© 2014 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2014 August 19. Received 2014 August 18; in original form 2014 June 20. The OVRO programme is supported in part by NASA grants NNX08AW31G and NNX11A043G and NSF grants AST-0808050 and AST-1109911. Support from MPIfR for upgrading the OVRO 40 m telescope receiver is acknowledged. WMthanks Jeffrey Scargle, James Chiang, Iossif Papadakis and Glenn Jones for discussions. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities Inc. TH was supported in part by the Jenny and AnttiWihuri foundation and by the Academy of Finland project number 267324. We thank the anonymous referee for constructive comments that greatly improved the presentation of some sections of this paper.
Published - MNRAS-2014-Max-Moerbeck-437-59.pdf
Submitted - 1408.6265v1.pdf