Empirical study and construction of stochastic processes on the long memory property of the time series of trade signs in a stock market.

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We study the influence of the trader's investment strategy on the long memory property of the time series of trade signs in a stock market, using the stochastic process. We present a discrete time stochastic process for polymer model which describes trader's trading strategy to split his or her order into small pieces, and prove that its scaled process converges to superposition of multiple fractional Brownian motions with different Hurst exponents and a standard Brownian motion. We also show that their Hurst exponents are derived from the distribution of the time interval of split orders.