中国股票市场的随机尖点突变模型

Stochastic cusp catastrophe model for Chinese stock market

采用最新的随机突变建模技术对中国股市建模.通过对自变量的筛选,分别对上证指数和深证综指给出了不同的模型.对历史数据的滚动窗口检验显示,两市优选出的突变模型在数据解释力上均要优于线性模型和伪突变的Logistic模型;中国股市不仅存在预期的不对称性,在特殊的时期还存在交易行为和市场情绪的分化特征.另外,沪市的随机尖点突变特征较深市更为明显,不过这些特征在近年已趋于减弱,表明市场正逐渐成熟.

A stochastic cusp model for Chinese stock market is established. After selecting the variables, two different models are set up to characterize Shanghai Stock Index and Shenzhen Composite Index respectively.Model calibrations based on a consistent Cobb＇s MLE method and corresponding statistical tests by sliding windows for historical data show that our optimal models outperform both linear regression model and nonlinear logistic model, which does not posses degenerate critical points but can mimic the sudden transition of the cusp. The empirical tests suggest that, in Chinese stock market, there exist not only asymmetric beliefs in a bull or bear market, but also strong bifurcations of trading behaviors and sentiment during periods of large fluctuations, bubble accumulation and bubble bursting. In addition, the Shanghai＇s stock cusp model fits better than Shenzhen＇s stock cusp model does. However, the Shanghai＇s stock model becomes weaker in distinguishing bifurcation behavior from the cusp model and logistic one in recent years, which implies the market is in the evolution of gradual rationalization.