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Real-time monitoring with RCA models
Methodology · Submitted 18 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our simulations show that our procedures, especially when standardising the CUSUM process, can ensure very good size control and short detection delays.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.79 | 0.92 | 0.12 | asserted 0.97 |
| s1 | 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. | result 0.94 | 0.96 | 0.19 | asserted 1.00 |
| s2 | In addition to considering the standard RCA model with no covariates, we also extend our results to the case of exogenous regressors. | contribution 0.89 | 0.92 | 0.04 | asserted 1.00 |
| s3 | 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. | result 0.70 | 0.80 | 0.16 | asserted 1.00 |
| s4 | Hence, our methodology is particularly suited to detect the onset, or the collapse, of a bubble or an epidemic. | interpretation 1.00 | 0.31 | 0.20 | asserted 0.89 |
| s5 | Our simulations show that our procedures, especially when standardising the CUSUM process, can ensure very good size control and short detection delays. | result 1.00 | 0.97 | 0.28 | asserted 0.88 |
| s6 | We complement our theory by studying the online detection of breaks in epidemiological and housing prices series. | contribution 0.91 | 0.94 | 0.10 | asserted 0.97 |
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The paper
Original abstract
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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How the literature uses it
2 arXiv papers cite this in 6 sentences
Papers citing it · 3 sentences without a confident label
Builds on it 1 paper
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The theory developed in [ref] paves the way to a more general research question, namely developing sequential monitoring techniques which are robust to both the initial regime (i.e., which can be employed irrespective of whether the observations in the training/historical sample are stationary or explosive), and to the type of change which occurs after a changepoint (i.e., which can detect changes from stationarity to another stationary regime, or to a explosive regime; or from an explosive regime to another explosive regime or a stationary one).
Sequential monitoring for explosive volatility regimes · Introduction · 0.80
Cites it as background 1 paper
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Several recent contributions also propose statistics based on the CUSUM process - as a leading example, which is drawing more and more attention in the literature, [ref] , [ref] , [ref] , and [ref] , study a standardised version of the CUSUM process (called the “Page-CUSUM”) based on comparing the average during the training period with the average computed during the monitoring period using a moving window, and choosing the length of such a window in order to maximise the discrepancy between the two averages in order to ensure an “optimal” detection delay when a changepoint is present.
Fast Online Changepoint Detection · Introduction · 0.93
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