## 1 Introduction  
In many fields of science, and especially in the study of complex systems, a very important problem is the possible interconnection between two point processes. In simple words, when we have two event time-series how can we decide that they influence one another? To answer this crucial question, [PERSON] et al. [1] recently introduced the event coincidence analysis (ECA) which takes the general viewpoint of possibly coupled point processes and quantifies the strength, directionality, and time lag of the statistical relations between these two event series. This is done by comparing the empirical co-occurrence frequencies with those one may expect for a null hypothesis model, e.g., uncoupled Poisson processes [2]. ECA has already found useful applications in various disciplines from epidemiology [1] and biogeography [3] to environmental and sustainability science [4], hydrology [5, 6], geophysics [7, 8], or even complex network physics [2]. Here, we employ ECA together with natural time analysis (NTA) to attack a problem related with the physics behind the preparation of strong earthquakes (EQs) which are one of the deadliest natural disasters.  
Natural time is a time domain, introduced in 2000s [9, 10], which provides the general setting for the NTA method [11] of the study of time-series emerging from complex systems. In NTA, only the order of events and their energy are considered, this way new interesting properties of the complex system emerge, which are hidden when using conventional time. It has been shown that natural time is optimal for reducing signals' uncertainty in time-frequency space (see, e.g., Section 2.6 of [11]). NTA has found applications in a wide variety of fields ranging from cardiology (see, e.g., [12, 13, 14, 15]) to statistical physics (see, e.g., [16, 17, 18, 19, 20, 21]), and atmospheric science (see, e.g., [22, 23, 24]). One of the main applications of NTA, however, is the study of the physics of EQs (see, e.g., [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 10, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118,  
time is considered as the basis of the \"nowcasting earthquakes\" methodology that has been introduced recently [38; 39; 40; 41; 42; 43; 44; 45; 46]. Furthermore, NTA has provided [26] a quantity, i.e., the variance of natural time, labeled \(\kappa_{1}\), which may serve as an order parameter for EQs cf. the latter may be considered as critical phenomena [11; 47; 48; 49; 50; 51; 52; 53; 54; 55]. The study of the fluctuations of \(\kappa_{1}\) before strong EQs revealed the existence of characteristic precursory minima [56; 57] that have been determined when studying either the regional or the global seismicity [30; 58; 59; 60; 61; 62]. It is the scope of the present work to employ the very recent tool of ECA for the investigation of the statistical significance of such minima.  
The present paper is organized as follows. In the next Section, we briefly summarize the background of NTA (Section 2.1) and ECA (Section 2.2). Section 3 presents the results obtained for both regional (Sections 3.1 and 3.2) and global (Section 3.3) seismicity. These results will be discussed in Section 4 and our conclusions follow in Section 5.