中国股市泡沫破裂临界时点动态置信区间研究

本文在对数周期幂率(LPPL)模型基础上，分别构建了“滚动窗口”以及“固定起点并移动终点”两种泡沫临界点动态置信区间构建方法，并以中国股市沪深300指数在2007年和2015年发生的两次大牛市股市崩盘为研究对象，采用两种新的方法进行样本外预测，计算出泡沫破裂的临界时点以及动态置信区间。研究结果表明，随着时间的不断推移，泡沫破裂临界时点的置信区间基本上能稳定覆盖实际发生泡沫破裂的时点。相比单纯利用LPPL模型预测临界时点方法，置信区间法能更好地克服预测临界时点随机性的情况，并能很好显示股市泡沫临界区间的变化轨迹，为投资者风险管理提供参考。

Dynamic Confidence Interval of the Critical Time of Chinese Stock Market Bubble Crash

Bubble refers to the explosive growth of asset prices, and the crash is rapidly decline of stock or stock index after the bubble bursts. A series of asset prices plummet in a short period of time causing a sharp oscillation in the stock market, which in turn damage the asset interests of investorsand disrupt the orderly development of the capital market.In this paper, a new method is developed through the Log-Periodic Power Law Model (LPPL) to help investors identify bubbles and track the risks of bubbles in financial activities effectively. The LPPL model is ln［p(t)］=A+(tc－t)α{B+Ccos［ωln(tc－t)+φ］}, where ln［p(t)］ is the logarithm of assets price, α is the exponent of the power law growth and tc is the critical point of bubble burst.The two big bull market crashes of the Shanghai and Shenzhen 300 Index (CSI 300) in 2007 and 2015 are studied. Based on the LPPL model, two methods including “rolling window” and “fixing the initial point and moving the end point” are introduced for resampling, then out-of-sample prediction daily is made to calculate the critical point of the bubble bursts and construct the dynamic confidence intervals for the bubble critical times respectively. Theempirical results show that the confidence interval of the critical times can basically cover the time when the bubbles crash actually occurs as time goes by. Compared with the simple method that use the LPPL model to predict the single critical time, the confidence interval method overcomes the randomness of the critical time prediction well, and also well display the change trajectory of the stock market bubble critical interval. The innovative method of this paper provides an effective tool for the risk management, which is a beneficial expansion for the researches of the crash early warning.