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On Similarity Measures for Stochastic and Statistical Modeling

Author

Listed:
  • Konstantinos Makris

    (Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, GR-15780 Athens, Greece
    These authors contributed equally to this work.)

  • Ilia Vonta

    (Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, GR-15780 Athens, Greece
    These authors contributed equally to this work.)

  • Alex Karagrigoriou

    (Laboratory of Statistics and Data Analysis, Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, GR-83200 Samos, Greece
    These authors contributed equally to this work.)

Abstract

In this work, our goal is to present and discuss similarity techniques for ordered observations between time series and non-time dependent data. The purpose of the study was to measure whether ordered observations of data sets are displayed at or close to, the same time points for the case of time series and with the same or similar frequencies for the case of non-time dependent data sets. A simultaneous time pairing and comparison can be achieved effectively via indices, advanced indices and the associated index matrices based on statistical functions of ordered observations. Hence, in this work we review some previously defined standard indices and propose new advanced dimensionless indices and the associated index matrices which are both easily interpreted and provide efficient comparison of the series involved. Furthermore, the proposed methodology allows the analysis of data with different units of measurement as the indices presented are dimensionless. The applicability of the proposed methodology is explored through an epidemiological data set on influenza-like-illness (ILI). We finally provide a thorough discussion on all parameters involved in the proposed indices for practical purposes along with examples.

Suggested Citation

  • Konstantinos Makris & Ilia Vonta & Alex Karagrigoriou, 2021. "On Similarity Measures for Stochastic and Statistical Modeling," Mathematics, MDPI, vol. 9(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:840-:d:534547
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    References listed on IDEAS

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    6. Félix Iglesias & Wolfgang Kastner, 2013. "Analysis of Similarity Measures in Times Series Clustering for the Discovery of Building Energy Patterns," Energies, MDPI, vol. 6(2), pages 1-19, January.
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