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运用分形理论探讨证券市场的自相似性与标度不变性 ,分析三种标度指数 ,即自相关指数、Hurst指数、基于 DFA算法的标度指数 .基于标准差时间序列改进 Hurst指数 ,将 DFA推广为动态递推算法 .利用三种标度指数对国内沪深股市进行实证研究 .结果表明 ,沪深股市收益率均不服从正态分布 ,在跨时间尺度的股价指数之间存在着相关性 ,表现为分形时间序列 ,说明其背后所隐含的政策导向影响中国股票市场的特征 .
Using the fractal theory to explore the self-similarity and scale invariance of the stock market, we analyze three kinds of scale index, namely the autocorrelation index, Hurst index and DFA algorithm based on the scaling index.We improve the Hurst index based on the standard deviation time series, Which is a dynamic recursive algorithm.We use three kinds of scale indexes to do an empirical research on the domestic stock markets in Shanghai and Shenzhen stock markets.The results show that the returns of the Shanghai and Shenzhen stock markets do not obey the normal distribution and there is a correlation between the price indexes across time scales , Showing a fractal time series, indicating that the implied policy direction behind it affects the characteristics of China’s stock market.