Figure 2
From: Maximum entropy approach to multivariate time series randomization
Comparisons between empirical PDFs (shown as histograms), CDFs and survival functions (CCDFs) and their empirical counterparts reconstructed with our ensemble approach from the Hamiltonians in Eq. (3), shown in yellow (\(H_1\)) and red (\(H_2\)), respectively. (a) Results on the PDF obtained by calibrating the models on 40 data points. (b) Results on the PDF obtained by calibrating the models on 4000 data points. (c) Results on the CDF (and associated survival function) with models calibrated on 40 data points. (d) Results on the CDF (and associated survival function) with models calibrated on 4000 data points. In all plots the dashed black lines marked as “True” correspond to the analytical PDF, CDF and survival function (depending on the panel) of the synthetic data generating process (given by a mixture of a Gaussian and a Student-t, see main text). Vertical dashed lines correspond to the 0.25, 0.5, and 0.75 quantiles employed to calibrate the models. The results from the ensemble have been obtained by pooling together \(10^6\) time series independently generated from the ensemble.
