Fig. 4
From: Second-order control of complex systems with correlated synthetic data
Effective correlations obtained on synthetic data. Dots represent estimated correlations on a synthetic dataset corresponding to 6 months between June and November 2015 (error-bars give 95% confidence intervals obtained with standard Fisher method); scale color gives the filtering frequency \(\omega _1=10\, \text {min},30\, \text {min},1\, \text {h},2\, \text {h},4\, \text {h}\); solid lines give the theoretical values for \(\rho _e\) obtained by 11 with estimated volatilities (dotted-line diagonal for reference); vertical red line position is the theoretical value such that \(\rho = \rho _e\) with mean values for \(\varepsilon _i\) on all points. We observe for high absolute correlations values a deviation from corrected values, what should be caused by non-verified independence and centered returns assumptions. Asymmetry is caused by the high value of \(\rho _0 \simeq 0.71\)