Distribution and Empirical Research of Asset Price Bubble Test under Recursive Mean Adjustment Mode

To improve the power of asset price bubble detection, the recursive mean adjustment method is applied to construct the PWY statistic and the distribution , critic values and size as well as power and empirical study of statistic under the specific data generation process are also analyzed. Theoretical research shows that the statistic converges to the functional of Wiener process in distribution under large sample, which is different from any of the existing statistic. Monte Carlo simulation shows that the critic values of recursive mean-adjusted statistic have both commonness and heterogeneity with that of existing statistic, as well as satisfactory size. When the sample size is small and the explosive degree is weak, the power is obviously superior. Specially, when the data is produced by several generation processes, the power is overall superior. The empirical research suggests that the recursive mean adjustment statistic can not only detect the existence of bubble in asset prices, but also identify the period when bubble occurs. The contribution of this paper is that it offers a new model for asset price bubble detection, and provides a new testing method for empirical research, which enriches the theory of asset price bubble detection.