## 1 Introduction  
The study of temporal properties of earthquakes contributes to analyzing the seismicity of a specific region in order to develop earthquake occurrence models. Earthquake occurrence is neither periodic nor completely random but often is clustered in both short- and long-term time scales [1, 2] represented by a complex summation of triggered (e.g., aftershocks of a strong earthquake or swarm-like excitations) and independently distributed (spontaneous) events. As a complex process, seismogenesis is characterized by scaling behavior [3], which is described by well-known empirical laws concerning the earthquake's magnitude distribution (the Gutenberg-Richter Law; [4]) and the aftershock's decay rate (the Omori Law; [5]). Focusing on the earthquake interevent time (\(\Delta T\)), [PERSON] et al. [6] stated that seismicity follows a universal scaling law, independently of the magnitude cut-off and the length of its spatial distribution. [PERSON] [7, 8] further studied this result and suggested that \(\Delta T\) is optimally described by the generalized Gamma distribution. Several studies (e.g., [9, 10], among others) questioned these findings and concluded that \(\Delta T\) distribution is deviated from universality. For example, [PERSON] et al. [11] examined both real and synthetic \(\Delta T\) and showed that a short \(\Delta T\) between consecutive earthquakes deviated from the unified scaling behavior as a result of the interaction between the triggered and spontaneous earthquakes. They concluded that the distribution of \(\Delta T\) is bimodal in a way that the correlated and independent earthquakes are following the Gamma distribution and exponential decay, respectively. In order to overcome these departures, [PERSON] [12] proposed a new expression of the \(\Delta T\) distribution, based on the Gamma distribution and included an additional parameter in its equation. The latter conclusions underline the impact of the correlations among \(\Delta T\), not only in terms of short-term clustering as the epidemic-type models (e.g., ETAS model; [13]) assume but in a more general way. This issue is becoming the main objective of several studies over the years. For instance, [PERSON] et al. [14] have investigated \(\Delta T\) data sets of six different earthquake catalogs worldwide with various magnitude thresholds and found that they are correlated, exhibiting behavior in which short \(\Delta T\) intervals are followed by short intervals and long \(\Delta T\) intervals are followed by large intervals. Applications of Detrended Fluctuations Analysis (DFA) and conditional probability methods in different study areas such as Northern and Southern California [15], Italy and Israel [16; 17] concluded similar results. Especially for Greece, [PERSON] et al. [18] applied DFA techniques for studying the memory of \(\Delta T\) for two distinctive fault zones of various magnitude thresholds, namely \(M_{thr}\geq 1.7\), \(M_{thr}\geq 2.3\), \(M_{thr}\geq 4.0\) and \(M_{thr}\geq 6.0\), and for the periods 2008-2014, 2008-2014, 1981-2014 and 1700-2014, respectively. They found that the \(\Delta T\) of small to moderate earthquakes exhibits strong long-range correlations whereas the \(\Delta T\) data sets of large earthquakes (\(M\geq 6.0\)) could be considered statistically independent. [PERSON] and [PERSON] [19] found that the \(\Delta T\) of global earthquakes (M-8) that occurred between 1900 and 2011, which might be considered rare events, are characterized by a lack of memory and can be described by a Poisson process. Given the aforementioned findings, the detection of any correlations between \(\Delta T\) or the existence of memory among them is an important characteristic of their temporal behavior.