Backward CUSUM for Testing and Monitoring Structural Change

Sven Otto and Jörg Breitung ()

VfS Annual Conference 2020 (Virtual Conference): Gender Economics from Verein für Socialpolitik / German Economic Association

Abstract: It is well known that the conventional CUSUM test suffers from low power and large detection delay. We therefore propose two alternative detector statistics. The backward CUSUM detector sequentially cumulates the recursive residuals in reverse chronological order, whereas the stacked backward CUSUM detector considers a triangular array of backward cumulated residuals. While both the backward CUSUM detector and the stacked backward CUSUM detector are suitable for retrospective testing, only the stacked backward CUSUM detector can be monitored online. The limiting distributions of the maximum statistics under suitable sequences of alternatives are derived for retrospective testing and fixed endpoint monitoring. In the retrospective testing context, the local power of the tests is shown to be substantially higher than that for the conventional CUSUM test if a single break occurs after one third of the sample size. When applied to monitoring schemes, the detection delay of the stacked backward CUSUM is shown to be much shorter than that of the conventional monitoring CUSUM procedure. Moreover, an infinite horizon monitoring procedure and critical values are presented.

Keywords: structural breaks; recursive residuals; sequential tests; change-point detection; local power; local delay (search for similar items in EconPapers)
JEL-codes: C12 C13 C32 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-ore
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