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Our aim is to investigate the possible physical association between consecutive coronal mass ejections (CMEs). Through a statistical study of the main characteristics of 27761 CMEs observed by SOHO/LASCO during the past 20 years. We found the waiting time (WT) or time elapsed between two consecutive CMEs is $< 5$ hrs for 59\% and $< 25$ hrs for 97\% of the events, and the CME WTs follow a Pareto Type IV statistical distribution. The difference of the position-angle of a considerable population of consecutive CME pairs is less than $30^\circ$, indicating the possibility that their source locations are in the same region. The difference between the speed of trailing and leading consecutive CMEs follows a generalized Student t-distribution. The fact that the WT and the speed difference have heavy-tailed distributions along with a detrended fluctuation analysis shows that the CME process has a long-range dependence. As a consequence of the long-range dependence, we found a small but significative difference between the speed of consecutive CMEs, with the speed of the trailing CME being higher than the speed of the leading CME. The difference is largest for WTs < 2 hrs and tends to be zero for WTs > 10 hrs, and it is more evident during the ascending and descending phases of the solar cycle. We suggest that this difference may be caused by a drag force acting over CMEs closely related in space and time.