Sign-based unit root tests for explosive financial bubbles in the presence of deterministically time-varying volatility
Sign-based, robust unit-root tests for explosive bubbles that are valid under 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.
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BibTeX
@article{Harvey_2019, title={SIGN-BASED UNIT ROOT TESTS FOR EXPLOSIVE FINANCIAL BUBBLES IN THE PRESENCE OF DETERMINISTICALLY TIME-VARYING VOLATILITY}, volume={36}, ISSN={1469-4360}, url={http://dx.doi.org/10.1017/S0266466619000057}, DOI={10.1017/s0266466619000057}, number={1}, journal={Econometric Theory}, publisher={Cambridge University Press (CUP)}, author={Harvey, David I. and Leybourne, Stephen J. and Zu, Yang}, year={2019}, month=Mar, pages={122–169} }