Wavelet Analysis of the Population Growth in a Depopulation Context Within Two Balkans Countries

Abstract

Serbia and Bulgaria have been selected in order to demonstrate how the principles of wavelet engines are applied to real data for the population growth rate (POPG). The annual time series data are retrieved from the UN database covering the period from 1990 to 2021. The major part of relevant wavelet coefficients (those coefficients exceeding threshold bounds) are concentrated in the first few scales. It was observed that the more significant ‘‘wave’’ behavior over wavelet coefficients and scales for both countries was revealed with MODWT transformation in contrast to the discrete wavelet transform (DWT). The main use of the Multi-Resolution Analysis (MRA) was the separation of the ‘‘signal’’ of the original POPG series from its noise, at a specific decomposition level. In both countries persistent behavior in the POPG series was found. A proximate examination of the wavelet threshold noise series reveals moderate differences between the countries. The large outlying observation in 2020 is accurately identified for the POPG series of both countries. There is no doubt that the theoretical background presented in this study might be relevant for each of the countries within this study observing in one or the other way.