Time lag is a key feature of hidden temporal dependencies within sequential data. In many real-world applications, time lag plays an essential role in interpreting the cause of discovered temporal dependencies. Traditional temporal mining methods either use a predefined time window to analyze the item sequence, or employ statistical techniques to simply derive the time dependencies among items. Such paradigms cannot effectively handle varied data with special properties, e.g., the interleaved temporal dependencies. In this paper, we study the problem of finding lag intervals for temporal dependency analysis. We first investigate the correlations between the temporal dependencies and other temporal patterns, and then propose a generalized framework to resolve the problem. By utilizing the sorted table in representing time lags among items, the proposed algorithm achieves an elegant balance between the time cost and the space cost. Extensive empirical evaluation on both synthetic and real data sets demonstrates the efficiency and effectiveness of our proposed algorithm in finding the temporal dependencies with lag intervals in sequential data. © 2012 ACM.