Fig. 4
Heterogeneity in intra-day price fluctuations. a Price evolution of SPY on June 19th, 2013. b Inferred temporal evolution of the mean correlation (black line) and the corresponding parameter distribution (blue shading). Red line and dashed lines represent the average daily temporal evolution of the mean correlation and its inter-quartile range, respectively. c Inferred temporal evolution of the mean volatility (black line) and the corresponding parameter distribution (red shading). Blue line and dashed lines represent the average daily temporal evolution of the mean volatility and its inter-quartile range, respectively. d Minute-scale trading volume of SPY. e Joint distribution of correlation and volatility, based on the heterogeneous random walk model (black lines; blue shading) and the corresponding fit using analytical distributions (red lines). f Histogram of positive minute log-returns from the 2011 to 2015 of the exchange-traded fund SPY (green), together with the best fit Gaussian distribution of the data (blue line) and the simulated distribution of log-returns from the heterogeneous model (red line). g Auto-correlation functions of the two model parameters, correlation (blue) and volatility (red). h Parameter cross-correlation as a function of lag-time. Positive lag-times correspond to a comparison of future volatility values to current correlation values. The shading in g, h corresponds to 1 s.e.m.
