基于小波的金融危机时点探测与多重分形分析

摘要

The market dynamics exhibits extremely turbulent behaviors around the financial crisis point. The correct locating of financial crisis point is the key step of distinguishing the multifractal properties of stock mar-ket both before and after financial crisis. Comparing with other methods,the wavelet transform modulus maxi-ma(WTMM)method has its advantages in detecting the outliers and indentifying the multifractal properties in financial markets. The time points of financial crisis are identified though the maxima lines of DJI and TPX in-dices,which are estimated by WTMM. The multifractal analysis of DJI is further performed around the time points where the outliers are detected. From our analysis,the WTMM is found to be capable of not only on correctly locating the time point of financial crisis,but also characterizing the evolution of the multifractal fea-tures both before and after financial crisis. Our empirical results also verify the Fractal Market Hypothesis (FMH)on the causes of market crash and provide a new idea for financial risk management.%在金融危机时点前后，市场的动力学会呈现出异常剧烈的波动。准确定位金融危机时点是区分出金融危机前后股市多重分形特性的关键步骤。与其他方法相比，小波变换模极大值法（WTMM）的优势在于它可以侦测出突变点并对金融市场的多重分形特性进行分析。研究通过小波变换模极大值法（WTMM）所建立的模极大值线将道琼斯工业指数（DJI）与东京证交所股价指数（TPX）的金融危机时点定位出来，随后基于所侦测出来的道琼斯工业指数（DJI）突变点对该指数进行多重分形分析。分析发现：小波变换模极大值法（WTMM）不仅可以准确定位金融危机发生的时点，还可以刻画出多重分形特征在金融危机前后的演化。实证结果验证了分形市场假说（FMH）关于市场发生崩溃的起因，也为金融风险管理提供了一个新思路。