度量股票市场情绪指数的新方法——基于状态空间模型

A New Method for Measuring the Stock Market Sentiment Index——Based on State Space Model

众所周知,市场参与者的整体情绪对市场走势有极大的影响,如何度量这一情绪的变化过程,进而研究其对证券市场的影响,有重要的意义.然而,迄今为止,尚无一个系统有效的方法直接度量股票市场的情绪指数.文章基于下面的基本事实:所谓的市场情绪指数虽然不可以直接观测度量,然而受其影响控制的股票指数却可以观测,而这正是状态空间模型研究的问题,因此文章选择在状态空间模型的框架下研究股票市场情绪指数的度量问题.核心思想是,将市场情绪指数作为状态变量,股票指数作为观测变量,建立状态空间方程组.在对模型中未知参数进行确定时,选用嵌入的EM算法,结合经典的Kalman滤波进行迭代,在迭代完成的同时,也给出了市场情绪指数的度量.

It is well known that sentiment index of stock market has great influence on market trends. However, there isn＇t a systematic and effective method to directly measure the stock market＇s sentiment index. As we know, sentiment index cannot be observed directly, but the stock index, whose trends are heavily influenced by the sentiment movement of the investors, are readily available in the stock market. Therefore, to employ the popular state space model by setting the sentiment index as the state variable and stock index as the observed variable is a natural choice to measure the unobserved sentiment index. In this paper, we first establish a state space model in the way above, then use EM algorithm together with Kalman filter to start an iterative process to estimate the unknown parameters in the model and evaluate the sentiment index. Thus we can estimate the unknown parameter in the model and obtain the stock market sentiment index at the same time.