Testing explosive bubbles with time-varying volatility

Harvey, David I.; Leybourne, Stephen J.; Zu, Yang

Abstract

This paper considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a weighted least squares-based variant of the Phillips, Wu and Yu (2011) test for explosive autoregressive behaviour. We find that such an approach has appealing asymptotic power properties, with the potential to deliver substantially greater power than the established OLS-based approach for many volatility and bubble settings. Given that the OLS-based test can outperform the weighted least squares-based test for other volatility and bubble specifications, we also suggested a union of rejections procedure that succeeds in capturing the better power available from the two constituent tests for a given alternative. Our approach involves a nonparametric kernel-based volatility function estimator for computation of the weighted least squares-based statistic, together with the use of a wild bootstrap procedure applied jointly to both individual tests, delivering a powerful testing procedure that is asymptotically size-robust to a wide range of time-varying volatility specifications.

Citation

Harvey, D. I., Leybourne, S. J., & Zu, Y. (2019). Testing explosive bubbles with time-varying volatility. Econometric Reviews, 38(10), 1131-1151. https://doi.org/10.1080/07474938.2018.1536099

• Journal Article Type: Article
• Acceptance Date: Aug 9, 2018
• Online Publication Date: Dec 20, 2018
• Publication Date: 2019
• Deposit Date: Aug 16, 2018
• Publicly Available Date: Dec 21, 2019
• Journal: Econometric Reviews
• Print ISSN: 0747-4938
• Electronic ISSN: 1532-4168
• Publisher: Taylor and Francis
• Peer Reviewed: Peer Reviewed
• Volume: 38
• Issue: 10
• Pages: 1131-1151
• DOI: https://doi.org/10.1080/07474938.2018.1536099
• Keywords: Rational bubble; Explosive autoregression; Time-varying volatility; Weighted least squares; Right-tailed unit root testing
• Public URL: https://nottingham-repository.worktribe.com/output/1036376
• Publisher URL: https://www.tandfonline.com/doi/abs/10.1080/07474938.2018.1536099?journalCode=lecr20
• Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Econometric Reveiews on 20 December 2018, available online: http://www.tandfonline.com/[10.1080/07474938.2018.1536099
• Contract Date: Aug 16, 2018