Long-range memory model of trading activity and volatility

Details Long-range memory model of trading activity and volatility Long-range memory model of trading activity and volatility

2006-06-14

arxiv.org/abs/physics/0606115v1

J. Stat. Mech. (2006) P10016

Physics

Physics and Society

12 pages, 5 figures

Scientific paper

10.1088/1742-5468/2006/10/P10016

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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