Estimating serial correlation and self-similarity in financial time series—A diversification approach with applications to high frequency data

Gerlich, Nikolas; Rostek, Stefan

doi:10.1016/j.physa.2015.03.085

Cited by 7 publications

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References 53 publications

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“…Similarly, the current value of the observable is influenced by its previous value. For example, the volatility of stock price may be the outcome of the influence of its past value [39][40][41][42][43]. More generally, such a process may be described by the delayed SDE [31] ( )…”

Section: Stochastic Dierential Equations With Variable Convention Pa...mentioning

confidence: 99%

Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations

2016

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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 dierential 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.

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