Lag patterns in time series databases

Time series motif discovery is important as the discovered motifs generally form the primitives for many data mining tasks. In this work, we examine the problem of discovering groups of motifs from different time series that exhibit some lag relationships. We define a new class of pattern called lagPatterns that captures the invariant ordering among motifs. lagPatterns characterize localized associative pattern involving motifs derived from each entity and explicitly accounts for lag across multiple entities. We present an exact algorithm that makes use of the order line concept and the subsequence matching property of the normalized time series to find all motifs of various lengths. We also describe a method called LPMiner to discover lagPatterns efficiently. LPMiner utilizes inverted index and motif alignment technique to reduce the search space and improve the efficiency. A detailed empirical study on synthetic datasets shows the scalability of the proposed approach. We show the usefulness of lagPatterns discovered from a stock dataset by constructing stock portfolio that leads to a higher cumulative rate of return on investment.