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In this paper, we empirically examine the volatility process of Korean stock market returns using the KOSPI200. To investigate the property of the process, we use the FIGARCH (Fractionally Integrated GARCH) model that includes GARCH and 1GARCH processes as special cases. Since the FIGARCH model allows fractional integration order, it can detect hyperbolically decaying volatility processes with cannot be explained by existing models with integer integration order. The result shows that the KOSPI200 exhibits long-term dependencies. To investigate the robustness of the obtained result, we analyze the time and cross-sectional aggregation effect using weekly data and individual stock returns that the KOSPI200 is comprised of. The long memory property of the KOSPI200 does not seem to be spuriously induced by aggregation.