Universität zu Köln

Breitung, Jörg ORCID: 0000-0001-7367-0863 and Diegel, Max (2025). Sequential Detector Statistics for Speculative Bubbles. Journal of Time Series Analysis, 46 (5). pp. 829-845. Wiley. ISSN 0143-9782

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Abstract

We propose a heteroskedasticity‐robust locally best invariant (LBI) statistic to test the hypothesis of a unit root against the alternative of an explosive root associated with speculative bubbles. Compared to existing alternatives such as Dickey‐Fuller type tests, the LBI statistic has a standard limiting distribution and greater power, particularly in the empirically relevant scenario of a moderately explosive root. Further refinements, such as the point‐optimal linear test, approach the power envelope remarkably closely. To detect bubbles with an unknown starting date, we consider sequential (CUSUM) schemes based on constant and time‐varying boundary functions, where the exponentially weighted CUSUM detector with a constant boundary function turns out to be most powerful. We also propose a simple method for date‐stamping the start of the bubble consistently. Finally, we illustrate our methods using two empirical examples.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Breitung, Jörg UNSPECIFIED https://orcid.org/0000-0001-7367-0863 UNSPECIFIED Diegel, Max UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-811064
Identification Number:	10.1111/jtsa.12845
Journal or Publication Title:	Journal of Time Series Analysis
Volume:	46
Number:	5
Page Range:	pp. 829-845
Number of Pages:	17
Date:	5 September 2025
Publisher:	Wiley
ISSN:	0143-9782
Language:	English
Faculty:	Faculty of Management, Economy and Social Sciences
Divisions:	Faculty of Management, Economics and Social Sciences > Economics > Econometrics and Statistics > Professorship for Statistics and Econometrics
Subjects:	Social sciences Economics
Uncontrolled Keywords:	Keywords Language explosive process ; LBI statistic ; monitoring ; speculative bubbles English
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/81106