## 4 Discussion
[86] that showed the interconnection of magnitude time series correlations with the minima of the fluctuations of the order parameter of seismicity and SES. Since References [13,86] were prepared almost simultaneously, these results have not been incorporated in the analysis of global seismicity [13]. Specifically, [PERSON] et al. [86] showed, among others, that during the observation of the fluctuation minimum in the regional study of Japan, the DFA exponent \(\alpha_{300}\) (obtained from the DFA, see Section 2.3, of segments of consecutive 300 EQs) reveals long-range correlations (cf. this fact was related to the SES properties and its generation mechanism [73,75,88]). Hence, studying the DFA of the magnitude time series should provide additional information on the quality of the 'precursory' fluctuation minima. For this reason, apart from \(\alpha_{300}\), we also calculated \(\alpha_{160}\) (since \(W=160\) is the largest window used in the NTA of global seismicity) and plot with the green broken line the quantity \(\langle\alpha\rangle=(\alpha_{160}+\alpha_{300})/2\) in Table 2.0 A close inspection of this Figure, together with the results shown in Table 1, indicates that \(\langle\alpha\rangle\) for the 'presursoy' fluctuation minima that precede the \(M\geq 8.5\) EQs lie in the narrow range 0.51-0.61. A comparison of these values with those obtained for the previous six false alarms eliminates four of them (see the bold face numbers in the last column of Table 1) leaving only FA1 and FA6 still as false alarms. To visually affirm this property, we depict in Figure 9 the values of \(\langle\alpha\rangle\) on the date of \(\beta_{160,min}\) for all the 'presursoy' fluctuation minima of Table 2.1 Thus, the present study reveals that when combining Conditions (10) and (11) with the additional condition:  
Table 2.2  
the NTA of global seismicity may identify order parameter fluctuation minima which are precursory (up to nine months before) for _all_ the strong EQs with \(M\geq 8.5\) with only two false alarms, i.e., those labeled FA1 and FA6 in Table 2.3 This is also supplemented, here, by an estimation of the future EQ epicenter location shown in Figures 5 and 6a,f. Table 2.4 Values of \(\langle\alpha\rangle\) for each of the ‘precursory’ fluctuation minima on the date of \(\beta_{160,min}\) of Table 2.5 The labels indicate whether they correspond to hit (H1 to H6, red bullets) or a false alarm (FA1 to FA6, blue circles). The dashed horizontal dashed red lines indicate the limits of Condition (14), i.e., 0.51 and 0.61, which when applied, validates all hits, while only FA1 and FA6 remain as false alarms. We now turn to the statistical significance of the proposed method, which will be estimated by means of ROC, see Section 2.6. Our data, spanning from 1 January 1976 to the end of January 2022, consist of 553 months, which include 61 nine-month periods, plus an extra period of four months, which will be disregarded from the following calculations. The reason we choose a period of nine months is because, as already mentioned, the variability minima in the GCMT catalog have [13] a maximum lead time of nine months. Thus, we apply the ROC method by dividing the first 549-month period of the studied catalog into 61 nine-month periods so that \(P+Q=61\). These periods, in our case, include only 6 EQs with \(M\geq 8.5\), i.e., \(P=6\), a fact that translates to 100% hit rate (we clarify that if we decrease the target threshold to 7.8, instead of 8.5, the hit rate would be lower than 100%, see also Appendix A of [PERSON] et al. [13]). The false alarm rate, on the other hand, is equal to \(6/55=10.91\%\). Using the fortran code VISROC.f of Reference [121], we obtain in Figure 10, the ROC diagram where we depict, with the orange circle, the operation point that corresponds to our results, alongside the probability \(p\) to obtain this point by chance which is 0.0053%.