Assessing the Quality of Time Series Clustering Using a Permutation Test.

One of the most important problems for research is the problem of time series clustering. Clustering is important in the tasks of identifying common dynamic changes between series and searching for patterns in the behavior of dynamics and, finally, for forecasting. The article discusses the problem of assessing the statistical significance of clustering. Currently, there are a number of approaches to assessing significance. These include asymptotic criteria, as well as criteria based on comparison of clustering results on analyzed groups with clustering results on simulated data, which are generated on the basis of the null hypothesis of group homogeneity. However, these approaches cannot be used to solve many time series clustering problems because of the difficulty of proving that convergence conditions are met and because of the difficulty of choosing an adequate null hypothesis and specification of the distribution from which the data are generated. The paper proposes an alternative approach designed to assess the significance of hierarchical agglomerative clustering using the maximum of a set of correlation coefficients calculated for different time lag values as a measure of similarity between time series. The approach is based on comparing the clustering results obtained from the original lagged correlation matrix with the clustering results obtained from the original one by random permutations of off-diagonal elements while maintaining symmetry. The paper presents the results of applying the developed method to the problem of temporal clustering, containing the values of the daily increase in the number of COVID-19 illnesses. [ABSTRACT FROM AUTHOR]