The Analysis of Variability of Short Data Sets Based on Mahalanobis Distance Calculation and Surrogate Time Series Testing

Abstract

In this work, we present convenient for short time series approach which is based on the multivariate Mahalanobis distance calculation, combined with the surrogate time series testing. In order to test the ability of this approach to differentiate changes which could occur in complex processes, we analyzed data sets of different origins. We used seismological, meteorological, physiological, and economic data sets. Exactly, we analyzed data sets of inter earthquake times (IET), inter earthquake distances (IED), and differences in consecutive magnitudes (DM) compiled from southern Californian earthquake catalogue, data sets of yearly number of warmer and colder days derived from maximal air temperature data bases in Tbilisi, Georgia, arterial systolic, and diastolic blood pressure time series of healthy persons, as well as components of Index of Economic Freedom (IEF) and exchange rate time series of three southern Caucasian countries. It was shown that used approach, even in the case of relatively short time series, may effectively be used to quantify dynamical changes occurred in different natural complex processes.