On Similarity Measures for Stochastic and Statistical Modeling

Konstantinos Makris, Ilia Vonta and Alex Karagrigoriou
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Konstantinos Makris: Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, GR-15780 Athens, Greece
Ilia Vonta: Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, GR-15780 Athens, Greece
Alex Karagrigoriou: Laboratory of Statistics and Data Analysis, Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, GR-83200 Samos, Greece

Mathematics, 2021, vol. 9, issue 8, 1-16

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.

Keywords: similarity measures; time series; dimensionless indices; index matrices; multivariate indices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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