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Clustering of interval time series

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Abstract

Interval time series occur when real intervals of some variable of interest are registered as an ordered sequence along time. We address the problem of clustering interval time series (ITS), for which different approaches are proposed. First, clustering is performed based on point-to-point comparisons. Time-domain and wavelet features also serve as clustering variables in alternative approaches. Furthermore, autocorrelation matrix functions, gathering the autocorrelation and cross-correlation functions of the ITS upper and lower bounds, may be compared using adequate distances (e.g. the Frobenius distance) and used for clustering ITS. An improved procedure to determine the autocorrelation function of ITS is proposed, which also serves as a basis for clustering. The different alternative approaches are explored and their performances compared for ITS simulated under different setups. An application to sea level daily ranges, observed at different locations in Australia, illustrates the proposed methods.

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Notes

  1. In what follows we omit the index t, for simplifying the notation.

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Acknowledgements

The work of P. Teles and P. Brito is financed by the ERDF—European Regional Development Fund—through the Operational Programme for Competitiveness and Internationalisation—COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”—and by the National Funds through the FCT—Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology)–as part of project UID/EEA/50014/2013. We thank the associate editor and reviewers for their helpful comments and suggestions.

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  1. Monash University, Melbourne, Australia

    Elizabeth Ann Maharaj

  2. Faculdade de Economia and LIAAD INESC TEC, Universidade do Porto, Porto, Portugal

    Paulo Teles & Paula Brito

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  1. Elizabeth Ann Maharaj
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Maharaj, E.A., Teles, P. & Brito, P. Clustering of interval time series. Stat Comput 29, 1011–1034 (2019). https://doi.org/10.1007/s11222-018-09851-z

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