基于Kalman滤波方法的证券市场噪音收益度量

Noise Return Measurement of Security Market Based on Kalman Filter Method

在充分解析价格扩散过程的基础上，本文构建了融入时变噪音因素的新过程，并将其离散化后转换成状态空间模型。然后，利用Kalman滤波方法并借助EM算法估计未知参数，实现了有效度量噪音收益的目的。最后，以上证综指1991年1月4日至2012年2月24日的周数据为样本探析中国股市噪音收益情况，结果表明：期间中国股市的噪音收益水平处在-23．00％～83．51％，且存在右偏及尖峰特征，进一步分析表明投资者理性程度及监管是影响噪音收益的重要因素。

Based on fully understanding of price diffusion process, this paper builds a new price process that incorporates the time-varying noise factor, which is then converted into a state-space model after diseretization. Then we employ the Kalman-Filter method and EM algorithm to estimate the unknown parameters which can measure noise effectively. Finally make the data of SH000001 from 1991.1.4 to 2012.2.24 as the sample to explore noise return of Chinese stock market, the result show that the noise return of Chinese stock market is from -23.00% - 83.51%, and featured by right skew and high kurtosis, and the simple analysis approved that the rational degree of investors and regulations of government are the important factors of noise return.