Modeling long-range memory trading activity by stochastic differential equations
arXiv:physics/0608036 · doi:10.1016/j.physa.2007.02.012
Abstract
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity observed in the stock markets. We present a simple stochastic relation between the trading activity and return, which enables us to reproduce long-range memory statistical properties of volatility by numerical calculations based on the proposed fractal point process.
12 pages, 4 figures, APFA5 Proceedings
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- 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
- 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
- Long-range memory test by the burst and inter-burst duration distribution
- Point Processes Modeling of Time Series Exhibiting Power-Law Statistics
- Ising Model with Power Law Resetting
- Modeling non-stationarities in high-frequency financial time series