Scaling analysis of time series of stock market indices of transitional economies in the Western Balkans

Abstract

In this paper we have analyzed scaling properties of time series of stock market indices (SMIs) of developing economies of Western Balkans, and have compared the results we have obtained with the results from more developed economies. We have used three different techniques of data analysis to obtain and verify our findings: Detrended Fluctuation Analysis (DFA) method, Detrended Moving Average (DMA) method, and Wavelet Transformation (WT) analysis. Following extensive research in the area of econophysics of national and international stock markets, we were interested to contribute to this body of knowledge by analyzing the dynamics of market behavior of transitional economies in the Western Balkans, and to compare data from these emerging economies with data from more economically developed countries. Analyzes of stock market behavior of the emerging economies of South America, or the developing Asian or African markets have shown that the values of scaling exponents, calculated from the time series of stock market indices, could be used to estimate the efficiency of markets in question. With that in mind, by applying the theoretical approach of statistical physics, we aim to offer a new perspective on stock market dynamics in the Western Balkans and contribute to better understanding of the development process in the region's economies. We have found scaling behavior in all SMI data sets that we have analyzed. Scaling of SMI series changes from long-range correlated to slightly anti-correlated behavior, i.e. the appropriate scaling exponents decrease in value with the increase in growth and/or maturity of the economy the stock market is embedded in. Scaling exponents α, H, and β, corresponding to the DFA, DMA, and WT technique, all cross the 0.5 (and zero) line, marking this alteration. We also report the presence of effects of potential periodic-like influences on the SMI data that we have analyzed. One such influence is visible in all our SMI series, and appears at a period Tp ≈ 90 days. We propose that the existence of various periodic-like influences on SMI data may partially explain the observed difference in types of correlated behavior of corresponding scaling functions. The application of time-dependent scaling analysis (tdDMA) proved that these influences are of a complex type, that is, they can not be easily distinguished from a local correlations profile.