Statistical properties of the returns of stock prices of international markets

Abstract

We investigate statistical properties of daily international market indices of seven countries, and high-frequency S&P500 and KOSDAQ data, by using the detrended fluctuation method and the surrogate test. We have found that the returns of international stock market indices of six ;countries follow a universal power-law distribution with an exponent of zeta approximate to 3, while the Korean stock market follows an exponential distribution with an exponent of beta approximate to 0.7. The Hurst exponent analysis of the original return, and its magnitude and sign series, reveal that the long-term-memory property, which is absent in the returns and sign series, exists in the magnitude time series with 0.7 <= H <= 0.8. The surrogate test shows that the magnitude time series reflects the non-linearity of the return series, which helps to reveal that the KOSDAQ index, one of the emerging markets, shows higher volatility than a mature market such as the S&P 500 index.