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Clustering time series by linear dependency

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Abstract

We present a new way to find clusters in large vectors of time series by using a measure of similarity between two time series, the generalized cross correlation. This measure compares the determinant of the correlation matrix until some lag k of the bivariate vector with those of the two univariate time series. A matrix of similarities among the series based on this measure is used as input of a clustering algorithm. The procedure is automatic, can be applied to large data sets and it is useful to find groups in dynamic factor models. The cluster method is illustrated with some Monte Carlo experiments and a real data example.

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Acknowledgements

This research has been supported by Consejo Superior de Investigaciones Científicas (Grant No. ECO2015-66593-P) of MINECO/FEDER/UE. We thanks to professor Tomohiro Ando for making available their code and kindly answer some questions regarding the implementation.

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Authors and Affiliations

  1. Department of Statistics and Institute Flores de Lemus, Universidad Carlos III de Madrid, Getafe, Spain

    Andrés M. Alonso

  2. Department of Statistics and Institute UC3M-BS of Financial Big Data, Universidad Carlos III de Madrid, Getafe, Spain

    Daniel Peña

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  1. Andrés M. Alonso
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  2. Daniel Peña
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Correspondence to Andrés M. Alonso.

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Alonso, A.M., Peña, D. Clustering time series by linear dependency. Stat Comput 29, 655–676 (2019). https://doi.org/10.1007/s11222-018-9830-6

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