# What test statistic for the hypothesis that early events affect future events?

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?