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Time‐series clustering via quasi U ‐statistics
Author(s) -
Valk Marcio,
Pinheiro Aluísio
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2012.00793.x
Subject(s) - mathematics , series (stratigraphy) , cluster analysis , independent and identically distributed random variables , statistics , stationary process , time series , order of integration (calculus) , decomposition , algorithm , mathematical analysis , random variable , paleontology , biology , ecology
The problem of time‐series discrimination and classification is discussed. We propose a novel clustering algorithm based on a class of quasi U ‐statistics and subgroup decomposition tests. The decomposition may be applied to any concave time‐series distance. The resulting test statistics are proven to be asymptotically normal for either i.i.d. or non‐identically distributed groups of time‐series under mild conditions. We illustrate its empirical performance on a simulation study and a real data analysis. The simulation setup includes stationary vs. stationary and stationary vs. non‐stationary cases. The performance of the proposed method is favourably compared with some of the most common clustering measures available.