SIGN-BASED UNIT ROOT TESTS FOR EXPLOSIVE FINANCIAL BUBBLES IN THE PRESENCE OF DETERMINISTICALLY TIME-VARYING VOLATILITY
提出一种基于符号的检验方法，用于在时变波动率下检测金融数据中的爆炸性泡沫，相比原方法无需自举法控制规模，且在某些设定下功效更高，并可用于确定泡沫起止点。
This article considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a sign-based variant of the Phillips, Shi, and Yu (2015, International Economic Review 56, 1043–1077) test. Unlike the original test, the sign-based test does not require bootstrap-type methods to control size in the presence of time-varying volatility. Under a locally explosive alternative, the sign-based test delivers higher power than the original test for many time-varying volatility and bubble specifications. However, since the original test can still outperform the sign-based one for some specifications, we also propose a union of rejections procedure that combines the original and sign-based tests, employing a wild bootstrap to control size. This is shown to capture most of the power available from the better performing of the two tests. We also show how a sign-based statistic can be used to date the bubble start and end points. An empirical illustration using Bitcoin price data is provided.