Analysis of cyclical behavior and quantification of the level of development from time series of stock market returns

Abstract

We have analyzed cyclical behavior of the three types of stock market indexes (SMI) time series: data belonging to stock markets of developed economies, emerging economies, and of the underdeveloped or transitional economies. We have used two techniques of data analysis to obtain and verify our findings: the wavelet transformation (WT) spectral analysis to study SMI returns data, and the Hurst exponent formalism to study local behavior around market cycles and trends. We calculated WT power spectra for all our SMI series, and have searched for characteristic peaks (local maxima) that point to existence of cycles in our data. We found cyclical behavior in all SMI data sets that we have analyzed. Moreover, the positions and the boundaries of cyclical intervals that we found seem to be common for all markets in our dataset. We differentiated nine such periods in our SMI data. Our results show that measures like the relative WT energy content and the relative WT amplitude for the peaks in the small scales region could be used to partially differentiate levels of growth and/or maturity of market economies in our dataset. Finally, we propose a way to quantify and compare the level of development of a stock market, based on the Hurst scaling exponent approach. From the local scaling exponents calculated for our nine peak regions we have defined what we named the Development Index (HDI), which proved, at least in the case of our dataset, to be suitable to rank the SMI series that we have analyzed in three distinct groups. Further verification of this method remains open for future research.