  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.
