As the number and size of large timestamped collections (e.g. sequences of digitized newspapers, periodicals, blogs) increase, the problem of efficiently indexing and searching such data becomes more important. Term burstiness has been extensively researched as a mechanism to address event detection in the context of such collections. In this paper, we explore how burstiness information can be further utilized to enhance the search process. We present a novel approach to model the burstiness of a term, using discrepancy theory concepts. This allows us to build a parameter-free, linear-time approach to identify the time intervals of maximum burstiness for a given term. Finally, we describe the first burstiness-driven search framework and thoroughly evaluate our approach in the context of different scenarios.