基于小波领袖多重分形分析法的股市有效性及风险检测

大多数关于股票市场有效性测量与风险侦测的研究都是基于有效市场假说。从分形市场假说出发，本文首先应用小波领袖多重分析法刻画市场波动的多重分形特性来衡量市场的有效性，然后提出一种应用市场最大波动点集的分形维数（D（h_min））及其奇异性指数（h_min）的演化特征来检测金融风险的新方法。实证结果表明：中、美、日三国在不同时期市场的有效性具有明显差异，中国市场的有效性正逐步提高，而美日两国市场的有效性水平与金融危机的发生更为密切。研究发现该方法不但可以正确地定位出金融危机发生的时点，还可以较准确地对风险进行测量。研究结果对于如何提高市场有效性，提升不同投资期限投资者的风险管理水平提供了一些启示。

The Efficiency and Risk Detection of Stock Markets Based on Wavelet Leaders (WL)Multifractal Analysis

Most research about efficiency measurement and risk detection in stock markets are based on the Efficient Market Hypothesis (EMH). From the Fractal Market Hypothesis (FMH), wavelet leaders (WL) multifractal analysis is firstly employed to measure the market efficiency by describing the multifractal properties of market fluctuations. And then a new method is put forward to detect and measure the financial crisis by the fractal dimension (D(h_min)) and singularity (h_min) evolutions of the largest fluctuations in the stock markets. The empirical results show that the efficiencies of China, United States and Japan stock markets differ from each other apparently during the different periods. The efficiency of China stock market has been improved gradually, while the efficiencies of United States and Japan stock markets are more related to the financial crisis. Through the analysis, the method is found to have the power not only on correctly locating the time point of financial crisis, but also measuring the financial crisis precisely by the evolution of the multifractal parameters. Empirical results can provide some revelation about how to improve the stock market efficiency and the financial risk management ability for the investors of different investment horizons.