Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations. (20th May 2016)

• Record Type: Journal Article
• Authors: Kaulakys, B; Alaburda, M; Ruseckas, J
• Is Part Of: Journal of statistical mechanics. (2016:May)
• Publication Date: 2016-05-20
• Subjects: Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/05/054035
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: A well-known fact in the financial markets is the so-called 'inverse cubic law' of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.