Analysis of cyclical behavior in time series of stock market returns

TL;DR

This study investigates cyclical patterns in stock market index time series across different economies using wavelet spectral analysis and Hurst exponents, revealing common cycles and proposing a market development index.

Contribution

It introduces a novel approach combining wavelet spectra and Hurst exponents to analyze market cycles and develop a quantitative development index for stock markets.

Findings

Identified nine common cyclical periods across all markets analyzed.

Wavelet spectral properties can differentiate market growth levels.

Proposed a Development Index based on Hurst exponents to rank market development.

Abstract

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.