Table 1 Fraction of empirical moments compatible with their corresponding ensemble distribution at different significance levels specified in terms of quantiles (e.g., 0.01–0.99 denotes that the 1st and 99th percentiles of the ensemble distribution are used as bounds to determine whether the null hypothesis of an empirical moment being compatible with the ensemble distribution can be rejected or not). Note that the confidence intervals used to obtain these results have not been adjusted for multiple hypothesis testing. Doing so (e.g., via False Coverage Rate³¹) would further suppress the number of true positives, resulting an even larger fraction of moments being compatible with the ensemble distribution. Moments are calculated both for each stock and each trading day. In the last column, we also report, for each moment, the median relative error between the empirical value and its ensemble average.

From: Maximum entropy approach to multivariate time series randomization