Switching AR model for housing bubbles test

For detecting rational bubbles, via relaxing the coefficient constraints of switching regression model, the paper proposes a more efficient model, autoregressive (AR) switching model, and gives the estimation method. An application to seasonally Chinese housing price data in the first decade of 21 century shows the model is more efficient than switching regression model, and provides evidence of bubbles in Beijing and Shanghai, but no evidence of bubbles in Tianjin and Chongqing. Further more, the probabilities of being in survival state show that the real estate-related policies of Chinese government have ruled out bubbles in Beijing, but not in Shanghai. The proposed model can also be used to detect rational bubbles with regime switching structures in other assets.