Free congruence: an exploration of expanded similarity measures for time series data

TL;DR

This paper explores a broader similarity measure for time series data that considers statistical resemblance and pattern components regardless of order, showing promising results compared to traditional methods like Dynamic Time Warping.

Contribution

It introduces an expanded similarity measure for time series that accounts for statistical properties and pattern permutations, beyond conventional point-to-point distances.

Findings

Stronger statistical resemblance in decline years than DTW

Broader similarity measure captures non-ordered pattern similarities

Results vary with data and sample size

Abstract

Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often involve point-to-point distance measures including Euclidean distance and Dynamic Time Warping. Such similarity measures fundamentally require the fluctuation of values in the time series being compared to follow a corresponding order or cadence for similarity to be established. This paper is spurred by the exploration of a broader definition of similarity, namely one that takes into account the sheer numerical resemblance between sets of statistical properties for time series segments irrespectively of value labeling. Further, the presence of common pattern components between time series segments was examined even if they occur in a permuted order, which would not necessarily satisfy the criteria of more conventional point-to-point distance measures. Results were compared with those of Dynamic Time Warping on the same data for context. Surprisingly, the test for the numerical resemblance between sets of statistical properties established a stronger resemblance for pairings of decline years with greater statistical significance than Dynamic Time Warping on the particular data and sample size used.