  We review the decomposition method of stock return cross-correlations,
presented previously for studying the dependence of the correlation coefficient
on the resolution of data (Epps effect). Through a toy model of random
walk/Brownian motion and memoryless renewal process (i.e. Poisson point
process) of observation times we show that in case of analytical treatability,
by decomposing the correlations we get the exact result for the frequency
dependence. We also demonstrate that our approach produces reasonable fitting
of the dependence of correlations on the data resolution in case of empirical
data. Our results indicate that the Epps phenomenon is a product of the finite
time decay of lagged correlations of high resolution data, which does not scale
with activity. The characteristic time is due to a human time scale, the time
needed to react to news.
