Soft Matter and Complex Systems Seminar

We use a continuous-time random walk (CTRW) to model (i) market fluctuation data from times when traders experience excessive losses or excessive profits and (ii) the analogous Earthquakes fluctuation data. We analytically derive superstatistics that accurately model empirical market activity data (supplied by Bogachev, Ludescher, Tsallis, and Bunde) and Earthquakes data of Corral that exhibit transition thresholds. We measure the inter-event times between excessive losses, excessive profits, and Earthquake amplitudes by using the mean inter-event 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 power-law corrected by the lower incomplete gamma function, which asymptotically tends toward robustness but initially gives an exponential, and (ii) a power-law damped by the upper gamma function, which tends toward the power-law only during short inter-event 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 the stylized fact of volatility clustering. Moreover, 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.