The QQ-Plot plots sample quantiles from the interarrival distribution against "population quantiles" from the Mittag-Leffler distribution; a linear plot indicates a good fit. To see what "perfect agreement" looks like, see the simulated data.
Any pattern found in the empirical copula corresponds to a dependence pattern between a magnitude and its preceding interarrival time. The (current version of) the CTRE Model assumes no dependence (and none of the given datasets show any pattern).
The auto-correlation plot displays any dependencies in the bivariate series of interarrival times and magnitudes for different lags. There are some spurious correlations for short lags, for the solar flare and bitcoin data.
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