国际市场股票价格收益率的统计特性
Statistical Properties of the Returns of Stock Prices of International Markets
摘要：
本文利用去趋势波动方法和替代检验，对7个国家的国际市场日指数以及高频数据$S&P500$和KOSDAQ的统计特性进行了研究。我们发现，七个国家的国际股票市场指数的收益率遵循普适幂律分布的指数$ζ\approx 3$，而韩国股票市场遵循指数分布的指数$β\approx 0.7$。通过对原始收益率及其幅值和符号序列的Hurst指数分析，发现具有$0.7 \leq H \leq 0.8$的幅值时间序列具有长期记忆性，这是收益率和符号序列所不具备的。替代检验表明，幅度时间序列反映了收益率序列的非线性，这有助于揭示，KOSDAQ指数，新兴市场之一，表现出更高的波动性比成熟的市场，如{S&P} 500指数。
英文摘要：
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 seven countries follow a universal power-law distribution with an exponent of $ζ\approx 3$, while the Korean stock market follows an exponential distribution with an exponent of $β\approx 0.7$. 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 $0.7 \leq H \leq 0.8$. 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.
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