基于分形理论的上海证券市场有效性实证检验

The Empirical Test of the Efficiency in Shanghai Securities Market Based on Fractal Theory

证券市场的有效性越高,其支撑实体经济发展以及优化资金资源化配置的作用越强。分别以上海证券市场中的上证国债指数、上证基金指数、上证综合指数收益率和成交量增长率的日、周、月度的时间序列为样本构造价、量多个分形模型,假定Hurst指数为0.5的布朗运动是市场完全有效的标准,一方面通过R/S分析直接得到Hurst指数用以横向地比较国债市场、基金市场、股票市场的有效性;另一方面通过ARFIMA(p,d,q)模型的分形维数与Hurst指数之间的关系间接得到Hurst指数,用以在不同的利率调控周期的区间上纵向比较国债市场、基金市场、股票市场的有效性。分析表明目前上海证券市场是一个无效的分形市场,因此应致力于证券市场的有效性建设。

The higher the effectiveness of securities market is, the stronger the role of supporting tangible economic development and optimizing capital resource allocation is, This paper treats the three largest markets on trading volume and turnover in the Shanghai Securities Market--Shanghai Bond Market, the Shanghai Fund Market, the Shanghai monthly Stock Market as a microcosm of Chinese Securities market via multi-fractal model by daily, weekly and time series of yield and volume growth rate of SSE T-Bond Index, SSE Fund Index and the SSE Composite Index. Brownian motion means Hurst exponent is 0.5 which is assumed as the symbol of perfectly efficient market. On the one hand, by R / S analysis directly computes Hurst exponent and compare laterally the Hurst exponent of Shanghai Bond market, the Shanghai Fund market, Shanghai stock market to analyze the market efficiency; on the exponent, and compare longitudinally the Hurst exponent of Shanghai Bond market, the Shanghai Fund market, Shanghai stock market to analyze the market efficiency in benchmark interest rate adjustment cycle. In conclusions, Shanghai stock market is a fractal inefficient market.