On why and how statistical significance criteria can guide multivariate time series motif analysis

On Why and How Statistical Significance Criteria Can Guide Multivariate Time Series Motif Analysis Miguel G. Silva, Sara C. Madeira, Rui Henriques • MSig framework evaluates the statistical significance of motifs in multivariate time series. • MSig extends statistical tests towards multidimensional motifs and mixed variables. • MSig minimizes spurious discoveries and promotes motif search efficiency. • False positive and negative rates of state-of-the-art motif discovery algorithms are quantified. • MSig offers a way out of the persisting trade-off between false positive control and motif coverage. The modeling of real-world system dynamics is often challenged by the presence of non-periodic patterns, including stimuli-dependent physiological responses in health systems, event-elicited traffic flows in mobility systems, or news-driven interactions in societal systems. While motif discovery has proven effective in revealing recurring events from time series data, the presence of spurious patterns hampers this process. Moreover, existing statistical significance stances are limited to univariate symbolic series. To address this critical gap, this study proposes a statistical frame to assess the likelihood of motifs to deviate from null expectations in multivariate time series with arbitrary order and variable types. It includes a principled discussion on the application of binomial testing as a strategy to guide motif discovery and reduce the incidence of false positives, considering variable dependencies, temporal associations, and multi-hypothesis corrections. Results from real-world case studies suggest that current motif discovery algorithms are vulnerable to spurious patterns, with up to 60% false positive discoveries under normative search conditions. The proposed assessment can enhance existing motif discovery algorithms by minimizing the occurrence of spurious patterns, prioritizing pattern importance, and refining the search space to decrease computational complexity.