arXiv 5 Mar 2020 · Econometrics · publishedEconometric Theory (2022) · 13 citations (OpenAlex)
arXiv:2003.02682 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chu, C.-S. J., Stinchcombe, M., and White, H (1996) Monitoring structural change | 1.000 | 15 | 7 | 100% |
| 2 | Brown, R. L., Durbin, J., and Evans, J. M (1975) Techniques for Testing the Constancy of Regression Relationships Over Time | 1.000 | 9 | 5 | 100% |
| 3 | Dalla, V., Giraitis, L., and Phillips, P. C. B (2020) Robust tests for white noise and cross-correlation | 0.737 | 3 | 2 | 100% |
| 4 | Fremdt, S (2015) Page's sequential procedure for change-point detection in time series regression | 0.737 | 3 | 2 | 100% |
| 5 | Jiang, P. and Kurozumi, E (2019) Power properties of the modified CUSUM tests | 0.737 | 3 | 2 | 100% |
| 6 | Robbins, M., Gallagher, C., Lund, R., and Aue, A (2011) Mean shift testing in correlated data | 0.737 | 3 | 2 | 100% |
| 7 | Aue, A. and Horváth, L (2004) Delay time in sequential detection of change | 0.644 | 2 | 2 | 100% |
| 8 | Aue, A., Horváth, L., and Reimherr, M. L (2009) Delay times of sequential procedures for multiple time series regression models | 0.644 | 2 | 2 | 100% |
| 9 | Newey, W. K. and West, K. D (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix | 0.644 | 2 | 2 | 100% |
| 10 | Zeileis, A., Leisch, F., Kleiber, C., and Hornik, K (2005) Monitoring structural change in dynamic econometric models | 0.644 | 2 | 2 | 100% |
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