Universality of market superstatistics

Abstract

We use a continuous-time random walk (CTRW) to model market fluctuation data from times when traders experience excessive losses or excessive profits. We analytically derive "superstatistics" that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde) that exhibit transition thresholds. We measure the interevent times between excessive losses and excessive profits, and use the mean interevent time as a control variable to derive a universal description of empirical data collapse. Our superstatistic value is a weighted sum of two components, (i) a powerlaw corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential, and (ii) a powerlaw damped by the upper incomplete gamma function, which tends toward the power-law only during short interevent times. We find that the scaling shape exponents that drive both components subordinate themselves and a "superscaling" configuration emerges. We use superstatistics to describe the hierarchical activity when component (i) reproduces the negative feedback and component (ii) reproduces the stylized fact of volatility clustering. Our results indicate that there is a functional (but not literal) balance between excessive profits and excessive losses that can be described using the same body of superstatistics, but different calibration values and driving parameters.

Statistical Collapse of Excessive Market Losses

“…Note that using our microscopic model to simulate agent behavior [23,24] gives results very close to those predicted by Eq. (7).…”

“…This variable was used previously in the analogous context in connection with the q-exponential [5]. Moreover, we obtain the superscaling of the scaling variable ln R Q or the scaling of scaling, i.e., the scaling of the scaling exponent α Q (for details see [22]). Figure 2 shows the agreement between the predictions of (7) and the empirical data for IBM for R Q = 2, 5, 10, 30, and 70 (going from the bottom curve to the top one).…”

“…Table II shows the corresponding fits of quantities α Q and τ Q (Q) (for more empirical results see Ref. [22], especially Figs. 2 and 5 there).…”

Econophysics and sociophysics: Their milestones & challenges

“…The understanding of mechanisms generating consistent statistics has therefore become a central issue. It so happens that the mentioned above properties of interevent times are also an immanent feature of financial markets' tick data studied in recent decade [91,92,93,94,95,96,97]. Their distinct real (and not spurious) multiscaling and multifractality were found.…”

The Chern‐Simons Current in Systems of DNA‐RNA Transcriptions

“…In the modern researches of algebraic geometry [25] for time series data, there exists another approach which uses the spinor field [18,26] in the Kolmogorov space of the time series data [27] over the genetic code to represent the gene structure as the ghost [41,42] and the anti-ghost fields of the codon and the anti-codon. This is achieved in the frameworks of supersymmetry [44][45][46] and G-theory [19,22]. Result of the construction show that all the calculations over codon can be assumed as a new superspace of the time series representation of the gene structure [27,47] .…”