Long-range memory model of trading activity and volatility

V. Gontis and B. Kaulakys

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Abstract: 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.

Date: 2006-06
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Citations: View citations in EconPapers (10)

Published in J. Stat. Mech. (2006) P10016

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