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This study employs a new time series representation of persistence in conditional mean and variance to test for the existence of the long memory property in the currency futures market. Empirical results indicate that there exists a fractional exponent in the differencing process for foreign currency futures prices. The series of returns for these currencies displays long-term positive dependence. A hedging strategy for long memory in volatility is also discussed in this article to help the investors hedge for the exchange rate risk by using currency futures.

Using the ARFIMA-FIGARCH model, this paper studies the efficiency of the Japanese equity market by examining the statistical properties of the returns and volatility of the Nikkei 225. It shows that both follow a long-range dependence, which stands against the applicability of the efficient market hypothesis. The result is valid for all sample periods, suggesting that the Japanese market remains inefficient despite the recent equity market reform.