  An average instantaneous cross-correlation function is introduced to quantify
the interaction of the financial market of a specific time. Based on the daily
data of the American and Chinese stock markets, memory effect of the average
instantaneous cross-correlations is investigated over different price return
time intervals. Long-range time-correlations are revealed, and are found to
persist up to a month-order magnitude of the price return time interval.
Multifractal nature is investigated by a multifractal detrended fluctuation
analysis.
