Damped Oscillatory Behaviors in the Ratios of Stock Market Indices

Abstract

This article reviews a recent finding on the properties of stock market indices (Wu, Europhys Lett 97:48009, 2012). A stock market index is an average of a group of stock prices with equal or unequal weights. Different stock market indices derived from various combinations of stocks are not expected to have fixed relations among them. From analyzing the daily index ratios of Dow Jones Industry Average (DJIA), NASDAQ, and S&P500 from 1971/02/05 to 2011/06/30 using the empirical mode decomposition, we found that the ratios NASDAQ/DJIA and S&P500/DJIA, normalized to 1971/02/05, approached and then retained the values of 2 and 1, respectively. The temporal variations of the ratios consist of global trends and oscillatory components including a damped oscillation in 8-year cycle and damping factors of 7183 days (NASDAQ/DJIA) and 138,471 days (S&P500/DJIA). Anomalies in the ratios, corresponding to significant increases and decreases of indices, are local events appearing only in the time scale less than 8-year cycle. The converge of the dominant damped oscillatory component implies that representative stocks in the pair-markets become more coherent as time evolves. IntroductionThe study of financial systems using the concepts and theories developed in physics has attracted much attention in recent years . Such study have revealed interesting properties in financial data, which facilitate deeper understanding of the underlying mechanisms of the systems and are essential for sequent modelling. These include financial stylized facts [4, 7-9, 11, 23, 24], such as fat tails in asset return distributions, absence of autocorrelations of asset returns, aggregational normality, asymmetry between rises and falls, volatility clustering [10], phase clustering [13][14][15], and damped oscillation in ratios of stock market indices [22].

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