Unit Root Tests for Explosive Financial Bubbles in the Presence of Deterministic Level Shifts
Abstract
This paper considers the issue of testing for an explosive bubble in financial data in the presence of deterministic level shifts. We propose that the sign-based variant of the Phillips, Shi, and Yu (2015) test, first introduced in Harvey, Leybourne, and Zu (2019) has practical advantages against other commonly used methods employed to control for level shifts. The sign-based test does not require any pre-determination of jump location or magnitude in order to be used, and is robust in terms of size and power to the presence of shifts. We show that, asymptotically, while the PSY test statistic is dependant on both the number of shifts present and their respective magnitudes, the sign-based variant requires a weaker assumption of the number of shifts alone. Finite sample simulations show severe size distortions and loss of power for the original test, while the sign=based test diplays a high degree of robusteness to the presence of level shifts. An empirical illustration using high-frequency Bitcoin price data sampled in late 2018 is also provided.
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