  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 spectral analysis to
study SMI returns data, and the Hurst exponent formalism to study local
behavior around market cycles and trends. We have found cyclical behavior in
all SMI data sets that we have analyzed. Moreover, the positions and the
boundaries of cyclical intervals that we have 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 also report on the possibilities to differentiate
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 for the peaks in the small scales region could be
used for partial differentiation between market economies. Finally, we propose
a way to quantify 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, 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.
