交易活动与波动性的长程记忆模型
Long-range memory model of trading activity and volatility
摘要：
早先我们提出了随机点过程模型，它再现了各种自仿射时间序列，其功率谱密度S（f）标度为频率f的幂，并导出了具有相同长程记忆性质的随机微分方程。在这里，我们提出了一个随机微分方程作为一个动态模型的观察记忆的金融时间序列。连续随机过程再现了交易活动的统计特性，并作为建模等待时间，回报和波动性的背景模型。经验观察到的统计特性：幂律概率分布的指数和长距离记忆金融变量的功率谱密度与几个模型参数的相同值再现。
英文摘要：
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential equation as a dynamical model of the observed memory in the financial time series. The continuous stochastic process reproduces the statistical properties of the trading activity and serves as a background model for the modeling waiting time, return and volatility. Empirically observed statistical properties: exponents of the power-law probability distributions and power spectral density of the long-range memory financial variables are reproduced with the same values of few model parameters.
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