## 4 Application
### Identifying the Earthquake Interevent Time Correlations
Specifically, it is observed that the statistic of the test (Q\({}_{stat}\); blue lines in Figure 5) is much larger than the critical value (Q\({}_{critical}\); red lines in Figure 5) of the Chi-square distribution, and consequently, the null hypothesis that the \(\Delta T\) data samples are independent can be rejected up to \(M_{thr}\geq 4.8\) (Figure 5a-h). The \(\Delta T\) data samples in which the Q statistic is clearly smaller than the critical value is again one for the \(M_{thr}\geq 4.9\) earthquakes (Figure 5i), confirming the results of the _ACF_ and _PACF_ calculations. In this respect, the magnitude threshold above which the \(\Delta T\) data of the central Ionian Islands appear statistically independent is for the \(M_{thr}\geq 4.9\) earthquakes. Table 2 presents the results of the aforementioned workflow for the detection of the temporal crossover among correlated and statistically independent earthquakes for the 10 sub-areas. In all the 10 cases, the results of _ACF-PACF_ analysis are in excellent agreement with those of the Ljung-Box Q-test (the detailed results of both _ACF-PACF_ analysis and the Ljung-Box Q-test are given graphically in Appendix A). The temporal crossover of  
Figure 5: Statistics of Ljung–Box Q-test (blue lines) and the critical values for the \(X^{2}\) distribution (red lines) for central Ionian Islands (sub-area 2) for magnitude thresholds (\(M_{thr}\)) varying from 4.1 to 4.9 (subplots **a–i**). the earthquakes interevent times data ranges from \(M_{thr}\geq 4.7\) up to \(M_{thr}\geq 5.1\). The lower magnitude threshold (\(M_{thr}\geq 4.7\)) is observed in the southwest Aegean Sea and Peloponnese (sub-area 6), whereas the largest (\(M_{thr}\geq 5.1\)) in western Greece and Albania (sub-area 1). Two out of the ten sub-areas (western Hellenic Arc and northern Greece and Balkans) are exhibiting temporal crossover for \(M_{thr}\geq 4.8\) threshold. Similarly, the \(\Delta T\) data samples of sub-areas 2 and 7, namely the central Ionian Islands and Corinth Gulf, respectively, are statistically independent at \(M_{thr}\geq 4.9\) thresholds. The eastern Hellenic Arc, southeast Aegean Sea, central Greece and North Aegean Sea (sub-areas 4, 5, 8 and 9, respectively) are exhibiting a temporal crossover for earthquakes with \(M_{thr}\geq 5.0\). To support these results, the Detrended Fluctuations Analysis (DFA) is performed for all sub-regions and \(M_{thr}\) values, in which the ACF-PACF analysis and Ljung-Box Q-test are applied. Figure 6 summarizes the results of the calculation of the exponent \(\alpha\) for each sub-region versus the respective \(M_{thr}\) values. In all cases, a systematic decrease in the exponent \(\alpha\) with an increase in the magnitude threshold can be observed. In all cases, \(\alpha\) ranges from values that indicate strong positive correlations (around 0.8) to ones that reveal weaker correlations or statistically independent behavior (from 0.65 to 0.33). More specifically, exponent \(\alpha\) is obtaining values near 0.5 for the highest \(M_{thr}\) values (except in the case of sub-region 9, which is equal to 0.67). These latter results are in very good agreement with the initially presented ones of the ACF-PACF analysis and Ljung-Box Q-test.