Consider you observe a series of events occurring over time where an event's time is denoted by $t_i$ ($i=1,2,...$). That is, you observe a vector $t = (t_1, t_2, ..., t_k)$ for $k$ events. Your hypothesis is that early events will affect future events (against the null of independence). For example, events are random but after a quota (unknown to the analyst) has been reached you expect to observe no more events.
Suppose you collect iid samples, what statistic can you use to test your hypothesis?