Long-range memory model of trading activity and volatility

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.

12 pages, 5 figures

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Cited by in corpus (12)

• Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations
• Stochastic model of financial markets reproducing scaling and memory in volatility return intervals
• The class of nonlinear stochastic models as a background for the bursty behavior in financial markets
• Trading activity as driven Poisson process: comparison with empirical data
• Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets
• Spurious memory in non-equilibrium stochastic models of imitative behavior
• Interplay between endogenous and exogenous fluctuations in financial markets
• Understanding the nature of the long-range memory phenomenon in socioeconomic systems
• Bessel-like birth-death process
• Long-range memory test by the burst and inter-burst duration distribution
• Agent-based Versus Macroscopic Modeling of Competition and Business Processes in Economics and Finance
• Modeling non-stationarities in high-frequency financial time series