Super-exponential expansion model about recognition of housing market bubble: In case of all districts in Beijing and Shanghai

The housing price in China has been raising for recent years, and the average housing sale prices for in Beijing and Shanghai have remained the top two in China. Now the housing prices in Beijing and Shanghai are still in the ascending, which rises people's concern that whether or not there is bubble in Beijing and Shanghai's housing market. Based on the second-hand housing sale price of each district in Beijing and Shanghai, this paper sets up super-exponential bubble model with stochastic mean-reverting critical times to detect and recognize the bubble of the over housing market. The paper distinguishes different level of bubble expansion and different stability of accumulation, and inspects the critical times that the bubbles will burst. Employing this model, the empirical study for housing market of Beijing and Shanghai between Dec. 2007 and Oct. 2015 indicates that housing bubble can be detected and the strength as well as stability of bubbles among 29 districts be also measured. Finally, we use this model to find that different levels of speculation bubble exist among all the districts of Beijing and Shanghai.