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

利用随机过程研究了交易者的投资策略对股票市场交易信号时间序列的长记忆性的影响。提出了一个离散时间随机过程的聚合物模型，该模型描述了交易者将其订单拆分成小块的交易策略，并证明了其标度过程收敛于具有不同Hurst指数的多个分数布朗运动和一个标准布朗运动的叠加.我们还表明，他们的赫斯特指数来自分裂订单的时间间隔的分布。

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.