Ensemble vs. time averages in financial time series analysis

Seemann, Lars; Hua, Jia-Chen; McCauley, Joseph L.; Gunaratne, Gemunu H.

doi:10.1016/j.physa.2012.06.054

Cited by 14 publications

(24 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many experimental systems, however, are known to diffuse anomalously. Examples include cold atoms in dissipative optical lattices [1,2], motion in a crowded environment such as the cytoplasm of biological cells [3][4][5], blinking quantum dots [6][7][8], and intra-day trades in financial markets [9][10][11]. Understanding the nature of the dynamics of these systems that leads to anomalous diffusion is a topic of intense interest.…”

Section: Introductionmentioning

confidence: 99%

Anomalous diffusion and the Moses effect in an aging deterministic model

et al. 2018

View full text Add to dashboard Cite

We decompose the anomalous diffusive behavior found in an aging system into its fundamental constitutive causes. The model process is a sum of increments that are iterates of a chaotic dynamical system, the Pomeau-Manneville map. The increments can have long-time correlations, fat-tailed distributions and be non-stationary. Each of these properties can cause anomalous diffusion through what is known as the Joseph, Noah and Moses effects, respectively. The model can have either sub-or super-diffusive behavior, which we find is generally due to a combination of the three effects. Scaling exponents quantifying each of the three constitutive effects are calculated using analytic methods and confirmed with numerical simulations. They are then related to the scaling of the distribution of the process through a scaling relation. Finally, the importance of the Moses effect in the anomalous diffusion of experimental systems is discussed.

show abstract

Section: Introductionmentioning

confidence: 99%

Anomalous diffusion and the Moses effect in an aging deterministic model

et al. 2018

View full text Add to dashboard Cite

show abstract

“…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.…”

mentioning

confidence: 99%

Anomalous scaling of stochastic processes and the Moses effect

et al. 2017

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…So in order to obtain the empirical asymptotic bi-exponential tail of F (u) [20,19,17], we must have…”

Section: Scalingmentioning

confidence: 99%

“…Unfortunately, the available data are insufficient to determine the asymptotic behavior of this slow decay, as discussed in Refs. [20,52].…”

Section: Autocorrelationmentioning

confidence: 99%

“…The validity of this approach has been justified in Ref. [20] by comparing the statistical characterizations of time and ensemble averages in both empirical high-frequency foreign exchange data and simulated time series. This finding also validates the variable diffusion model used in simulation, in that it exhibits key stylized facts of markets.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation