2003MNRAS.344..798K

Two first-order autoregressive time-series are observed subject to considerable measurement error. One time-series is a scaled, lagged version of the other. The properties of the cross-correlation function between the two series are studied. Simulation results show that the sample cross-correlation function is biased substantially downward for sample sizes of even a few hundred. The theoretical derivations are applied to simultaneous optical and X-ray observations of the low-mass X-ray binary LMC X-2. It appears that the lag of maximum cross-correlation between the two sets of observations varied over a range of more than 30 s during the 1.22 h of data analysed here.