  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.
