  We study the long-term memory in diverse stock market indices and foreign
exchange rates using the Detrended Fluctuation Analysis(DFA). For all daily and
high-frequency market data studied, no significant long-term memory property is
detected in the return series, while a strong long-term memory property is
found in the volatility time series. The possible causes of the long-term
memory property are investigated using the return data filtered by the AR(1)
model, reflecting the short-term memory property, and the GARCH(1,1) model,
reflecting the volatility clustering property, respectively. Notably, we found
that the memory effect in the AR(1) filtered return and volatility time series
remains unchanged, while the long-term memory property either disappeared or
diminished significantly in the volatility series of the GARCH(1,1) filtered
data. We also found that in the high-frequency data the long-term memory
property may be generated by the volatility clustering as well as higher
autocorrelation. Our results imply that the long-term memory property of the
volatility time series can be attributed to the volatility clustering observed
in the financial time series.
