Large deviation events, like hurricanes or financial crises, can have severe consequences. When these events cluster, occurring close together, their impact intensifies. In our study of the moving average process under heavy-tailed distributions, we analyzed this clustering behavior. We found that the "conspiracy vs. catastrophe” distinction between light and heavy tailed distributions still applies. Using the "single large jump" intuition, we demonstrated that cluster sizes follow an approximately uniform distribution that grows linearly with sample size.