Lajos Horváth, Lorenzo Trapani
arXiv 18 Dec 2023 · Statistics — Methodology · publishedEconometric Theory (2025) · 1 citations (OpenAlex)
arXiv:2312.11710 · PDF · DOI · OpenAlex · Extracted main text
We propose a family of weighted statistics based on the CUSUM process of the WLS residuals for the online detection of changepoints in a Random Coefficient Autoregressive model, using both the standard CUSUM and the Page-CUSUM process. We derive the asymptotics under the null of no changepoint for all possible weighing schemes, including the case of the standardised CUSUM, for which we derive a Darling-Erdos-type limit theorem; our results guarantee the procedure-wise size control under both an open-ended and a closed-ended monitoring. In addition to considering the standard RCA model with no covariates, we also extend our results to the case of exogenous regressors. Our results can be applied irrespective of (and with no prior knowledge required as to) whether the observations are stationary or not, and irrespective of whether they change into a stationary or nonstationary regime. Hence, our methodology is particularly suited to detect the onset, or the collapse, of a bubble or an epidemic. Our simulations show that our procedures, especially when standardising the CUSUM process, can ensure very good size control and short detection delays. We complement our theory by studying the online detection of breaks in epidemiological and housing prices series.
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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 | Horváth, L. and L. Trapani (2023) Changepoint detection in heteroscedastic random coefficient autoregressive models | 1.000 | 17 | 6 | 100% |
| 2 | Berkes, I., L. Horváth, and S. Ling (2009) Estimation in nonstationary random coefficient autoregressive models | 0.928 | 4 | 3 | 100% |
| 3 | Aue, A., S. Hörmann, L. Horváth, and M. Husková (2014) Dependent functional linear models with applications to monitoring structural change | 0.874 | 7 | 2 | 100% |
| 4 | Horváth, L. and L. Trapani (2016) Statistical inference in a random coefficient panel model | 0.843 | 3 | 3 | 100% |
| 5 | Aue, A., L. Horváth, and J. Steinebach (2006) Estimation in random coefficient autoregressive models | 0.811 | 4 | 2 | 100% |
| 6 | Aue, A. and L. Horváth (2004) Delay time in sequential detection of change | 0.644 | 2 | 2 | 100% |
| 7 | Berkes, I., S. Hörmann, and J. Schauer (2011) Split invariance principles for stationary processes | 0.644 | 2 | 2 | 100% |
| 8 | Fremdt, S (2015) Page's sequential procedure for change-point detection in time series regression | 0.644 | 2 | 2 | 100% |
| 9 | Diba, B. T. and H. I. Grossman (1988) The theory of rational bubbles in stock prices | 0.511 | 2 | 1 | 100% |
| 10 | Hall, P. and C. C. Heyde (2014) Martingale Limit Theory and its Application | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 56 scored citations.