泡沫随机临界时点超指数膨胀模型:中国股市泡沫的检测与识别

Super-exponential bubble model with stochastic mean-reverting critical times:Application in Chinese stock market

传统的泡沫模型都是假设泡沫是指数膨胀的,无法显著地将泡沫和同样是指数增长的基本面引起的高速价格增长区分开来,使得泡沫检验的有效性遭到置疑.泡沫超指数膨胀模型可以克服这一缺陷,它认为泡沫是一种本质上快于指数增长的更快膨胀,具有一个理论上的有限时间终结点.引入了最新的一类超指数膨胀模型——均值回复平稳随机临界时点模型.它将泡沫的检验和识别转化为1)检测"非线性非平稳的股价序列是否潜含均值回复的平稳临界时点序列";2)估计正反馈效应指数和潜在临界时点.利用它对中国股市2005年中期至2007年后期的投机泡沫实证分析表明,该模型能够有效的检验中国股市泡沫的存在性,并能识别29个行业板块间泡沫的膨胀强度和稳定性大小.同时,模型对于中国股市的泡沫破灭也有良好的预警效果.最后分析了模型的政策含义.

Bubbles are often defined as exponentially explosive prices within traditional financial bubble models.These models are bearing criticism to be not able to effectively detect the bubbles because the exponentially growing price regime observed,which is defined as bubble,could also be rationalized by some possible fundamental valuation models.However,super-exponential growth bubble models can provide a clear distinguishing signature between bubble and fundamental growth.In this kind of models,the essence of bubble reflects the faster-than-exponential characteristics,which implies a theoretical finite termination time.This paper attempted to introduce a new super-exponential growth bubble model,which is called Stochastic Mean-Reverting Critical Times model.According to this model,detection and diagnostic of bubble were translated into i） testing existence of a stationary mean-reverting critical times series embedded in nonlinear non-stationary stock price series,ii） estimation of exponent for positive feedback effects and the potential critical time.Employing this model,the empirical study for Chinese stock market indicates that the 2005-2007 Chinese bubble can be detected;the strength as well as stability of bubbles among 29 industrial sectors be also measured.Meanwhile,this model suggests the feasibility of advance bubble warning for Chinese stock market.At the last,this paper discusses the policy implication for bubble precaution.