Sign-Based Unit Root Tests for Explosive Financial Bubbles in the Presence of Deterministically Time-Varying Volatility

Abstract

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.

Volatility Spillover and International Contagion of Housing Bubbles

“…While this similarity with Gomez-Gonzalez et al (2018) suggests accurate date stamping of bubble episodes, the GSADF test used in both studies is criticized. In fact, Monschang and Wilfling (2020) argued that while Phillips et al's (2015) GSADF test yields more accurate estimates of the bubbles' origination and termination dates compared to other methods such as the sign-based test statistic of Harvey et al (2020), the procedure might date-stamp non-existing bubbles. The results of Monschang and Wilfling (2020) also suggest that the dating strategies might be sensitive to the data frequency as well.…”

A new mechanism for anticipating price exuberance

“…Definitely, one can consider far more complicated learning rules. Finally, it is also possible to change the test statistic used to capture price acceleration (see, for example, Harvey, Leybourne, & Zu, 2019). Nonetheless, one should consider both effectiveness and efficiency of the choices.…”

Can news-based economic sentiment predict bubbles in precious metal markets?

“…PSY generalized the SADF test using large subsamples by changing the start and endpoints of the recursion over a feasible range of flexible windows. 7 Although the GSADF can effectively detect real-time bubbles in financial markets, it suffers from size distortions caused by heteroscedastic innovations (Harvey et al 2016 , 2019 , 2020 ) and the multiplicity issue of recursive testing (Phillips and Shi 2018 ). 8 Phillips and Shi ( 2020 ) addressed the potential impact of heteroscedasticity and multiplicity issues of recursive testing algorithms by developing a wild-bootstrap-based implementation of the GSADF test.…”