Framework for Variable-Lag Motif Following Relation Inference in Time Series Using Matrix Profile Analysis

Knowing who follows whom and what patterns they are following are crucial steps to understand collective behaviors (e.g., a group of human, a school of fish, or a stock market). Time series is one of the resources that can be used to get insight regarding following relations. However, the concept of following patterns or motifs and the solution to find them in time series are not obvious. In this work, we formalize a concept of following motifs between two time series and present a framework to infer following patterns between two time series. The framework utilizes one of the efficient and scalable methods to retrieve motifs from time series called the Matrix Profile Inference Method. We compare our proposed framework with several baselines. The framework performs better than baselines in the simulation datasets. In the dataset of sound recording, the framework is able to retrieve the following motifs within a pair of time series in which two singers sing following each other. In the cryptocurrency dataset, the framework is capable of capturing the following motifs within a pair of time series from two digital currencies, which implies that the values of one currency follow the values of another currency patterns. Our framework can be utilized in any field of time series to get insight regarding following patterns between time series. The code and datasets can be found at https://github.com/hughnaaek/Following-Motif-Relation .