Bubble testing under polynomial trends
研究了多项式趋势下自回归系数最小二乘估计的渐近理论，发现常用右尾单位根检验易误判为泡沫，提出基于AR(2)回归的新方法，能稳健区分多项式趋势与温和泡沫，应用于美国房地产市场发现传统方法标记的负泡沫并非真泡沫。
Summary This paper develops the asymptotic theory of the least squares estimator of the autoregressive (AR) coefficient in an AR(1) regression with intercept when data is generated from a polynomial trend model in different forms. It is shown that the commonly used right-tailed unit root tests tend to favour the explosive alternative. A new procedure, which implements the right-tailed unit root tests in an AR(2) regression, is proposed. It is shown that, when the data generating process has a polynomial trend, the test statistics based on the new procedure cannot find evidence of explosiveness. Whereas, when the data generating process is mildly explosive, the new procedure finds evidence of explosiveness. Hence, it enables robust bubble testing under polynomial trends. Empirical application of the proposed procedure using data from the US real estate market reveals some interesting findings. In particular, all the negative bubble episodes flagged by the traditional method are no longer regarded as bubbles by the new procedure.