Variable diffusion in stock market fluctuations

Hua, Jia-Chen; Chen, Lijian; Falcon, Liberty; McCauley, Joseph L.; Gunaratne, Gemunu H.

doi:10.1016/j.physa.2014.10.024

Cited by 11 publications

(3 citation statements)

References 57 publications

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“…Financial time series of exchange-traded funds (ETFs) were analyzed as an application of the methods introduced here. As has been found to be the case for other financial markets [23,40,41], the intraday prices of ETFs can be considered to be governed by non-stationary stochastic processes that repeat each trading day. We find two intervals where the underlying stochastic process scales anomalously with H = 1/2, which is often associated with a violation of the efficient market hypothesis (EMH).…”

Section: Discussionmentioning

confidence: 99%

“…In this subsection we introduce a set of diffusive processes whose increments depend on X t as well. Variable diffusion processes (VDPs) was introduced as a model for intraday variations in financial markets [23,40,41]. Here {X t , t ≥ 0} satisfies the stochastic differential equation: dX t = D[X t , t]dB t , where D(X t , t) is the diffusion coefficient.…”

Section: Variable Diffusion Processmentioning

confidence: 99%

“…They account for finite-time corrections to the scaling behavior, and will be applied to standard and scaled versions of example stochastic processes to highlight the roles played by H, L, J, and M . Finally, exponents for a model of intraday trading in financial markets, variable diffusion processes [23,[34][35][36][37][38][39][40][41], will be computed and compared to the results with an empirical analysis of financial market data.…”

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confidence: 99%

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Anomalous scaling of stochastic processes and the Moses effect

et al. 2017

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The state of a stochastic process evolving over a time t is typically assumed to lie on a normal distribution whose width scales like t 1 2 . However, processes where the probability distribution is not normal and the scaling exponent differs from 1 2 are known. The search for possible origins of such "anomalous" scaling and approaches to quantify them are the motivations for the work reported here. In processes with stationary increments, where the stochastic process is time-independent, auto-correlations between increments and infinite variance of increments can cause anomalous scaling. These sources have been referred to as the Joseph effect the Noah effect, respectively. If the increments are non-stationary, then scaling of increments with t can also lead to anomalous scaling, a mechanism we refer to as the Moses effect. Scaling exponents quantifying the three effects are defined and related to the Hurst exponent that characterizes the overall scaling of the stochastic process. Methods of time series analysis that enable accurate independent measurement of each exponent are presented. Simple stochastic processes are used to illustrate each effect. Intraday financial time series data is analyzed, revealing that its anomalous scaling is due only to the Moses effect. In the context of financial market data, we reiterate that the Joseph exponent, not the Hurst exponent, is the appropriate measure to test the efficient market hypothesis.

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Section: Discussionmentioning

confidence: 99%

Section: Variable Diffusion Processmentioning

confidence: 99%