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Time series similarity measures are highly relevant in a wide range ofemerging applications including training machine learning models,classification, and predictive modeling. Standard similarity measures for timeseries most often involve point-to-point distance measures including Euclideandistance and Dynamic Time Warping. Such similarity measures fundamentallyrequire the fluctuation of values in the time series being compared to follow acorresponding order or cadence for similarity to be established. This paper isspurred by the exploration of a broader definition of similarity, namely onethat takes into account the sheer numerical resemblance between sets ofstatistical properties for time series segments irrespectively of valuelabeling. Further, the presence of common pattern components between timeseries segments was examined even if they occur in a permuted order, whichwould not necessarily satisfy the criteria of more conventional point-to-pointdistance measures. Results were compared with those of Dynamic Time Warping onthe same data for context. Surprisingly, the test for the numerical resemblancebetween sets of statistical properties established a stronger resemblance forpairings of decline years with greater statistical significance than DynamicTime Warping on the particular data and sample size used.

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