Universität zu Köln

Otto, Sven and Breitung, Jörg ORCID: 0000-0001-7367-0863 (2023). BACKWARD CUSUM FOR TESTING AND MONITORING STRUCTURAL CHANGE WITH AN APPLICATION TO COVID-19 PANDEMIC DATA. Econometric Theory, 39 (4). pp. 659-692. NEW YORK: CAMBRIDGE UNIV PRESS. ISSN 1469-4360

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Abstract

It is well known that the conventional cumulative sum (CUSUM) test suffers from low power and large detection delay. In order to improve the power of the test, we propose two alternative statistics. The backward CUSUM detector considers the recursive residuals in reverse chronological order, whereas the stacked backward CUSUM detector sequentially cumulates a triangular array of backwardly cumulated residuals. A multivariate invariance principle for partial sums of recursive residuals is given, and the limiting distributions of the test statistics are derived under local alternatives. In the retrospective context, the local power of the tests is shown to be substantially higher than that of the conventional CUSUM test if a break occurs in the middle or at the end of the sample. When applied to monitoring schemes, the detection delay of the stacked backward CUSUM is found to be much shorter than that of the conventional monitoring CUSUM procedure. Furthermore, we propose an estimator of the break date based on the backward CUSUM detector and show that in monitoring exercises this estimator tends to outperform the usual maximum likelihood estimator. Finally, an application of the methodology to COVID-19 data is presented.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Otto, Sven UNSPECIFIED UNSPECIFIED UNSPECIFIED Breitung, Jörg UNSPECIFIED orcid.org/0000-0001-7367-0863 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-667596
DOI:	10.1017/S0266466622000159
Journal or Publication Title:	Econometric Theory
Volume:	39
Number:	4
Page Range:	pp. 659-692
Date:	2023
Publisher:	CAMBRIDGE UNIV PRESS
Place of Publication:	NEW YORK
ISSN:	1469-4360
Language:	English
Faculty:	Faculty of Management, Economy and Social Sciences
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language TIME-SERIES REGRESSION; INVARIANCE-PRINCIPLES; CHANGE-POINT; PARAMETER INSTABILITY; HETEROSKEDASTICITY; APPROXIMATION; POWER Multiple languages Economics; Mathematics, Interdisciplinary Applications; Social Sciences, Mathematical Methods; Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/66759