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The Long-term Correlation of Conditional Time Series of Financial Time Series

In this paper, the Hang Seng Index data for the 22-year period, from December 31, 1986, to June 6, 2008 in the Hongkong stock market, are analyzed. Using rescaled range method, the Hurst exponent is estimated for financial time series and empirical evidence suggests that such market possess strong long-range dependence for both conditional time series and volatility. In order to get more information of the conditional series, we study how the threshold value q affects the correlations of the conditional time series following a certain threshold q. We find that the correlations of the conditional time series grow stronger at the large threshold q.