Analysis of cyclical behavior in time series of stock market returns

In this paper we have analyzed scaling properties and 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 transform (WT) spectral analysis to identify cycles in the SMI returns data, and the time- dependent detrended moving average (tdDMA) analysis to investigate local behavior around market cycles and trends. 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 seam to be common for all markets in our dataset. We list and illustrate the presence of nine such periods in our SMI data. We report on the possibilities to differ-entiate between the level of growth of the analyzed markets by way of statistical analysis of the properties of wavelet spectra that characterize particular peak behaviors. Our results show that measures like the relative WT energy content and the relative WT amplitude of the peaks in the small scales region could be used to partially differentiate between market economies. Finally, we propose a way to quantify the level of development of a stock market based on estimation of local complexity of markets SMI series. From the local scaling exponents calculated for our nine peak regions we have defined what we named the Development Index, 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