Testing bubbles based on modified PWY method

In recent years, the identification and inspection of bubbles has appeared as an important research topic in the financial field. ADF testing method and the PWY alternative method are commonly used, with serial correlation in high-frequency financial time series. In order to remove the influence of serial correlation and be able to test the situation of multiple bubbles at the same sample period, we have made a correction to the PWY alternative method with serial correlation. The BSADF method is used to obtain the statistical sequence, and the corresponding modified critical value sequence is given based on the simulation one. According to the Shanghai Stock Index from 2000 to 2019, an empirical study was conducted based on the GSADF and the revised PWY method to identify and test the bubble phenomenon. The empirical results show that three bubbles appeared between 2000 and 2019, which is in line with the actual financial market conditions, and the traditional PWY method cannot detect all bubbles. Therefore, the GSADF and the modified PWY method given in this article can find bubbles in time and provide some guidance to identify market risks and prevent financial crises.