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REAL-TIME MONITORING WITH RCA MODELS

Published online by Cambridge University Press:  03 March 2025

Lajos Horváth  and
Lorenzo Trapani
Lajos Horváth
Affiliation:
University of Utah
Lorenzo Trapani*
Affiliation:
Universita’ di Pavia and University of Leicester
*
Address correspondence to Lorenzo Trapani, Department of Economics and Management, University of Pavia, Via San Felice al Monastero 5, 27100 Pavia, Italy, e-mail: lorenzo.trapani@unipv.it.
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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 standardized CUSUM, for which we derive a Darling–Erdös-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.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 34
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

We are grateful to the Editor, P.C.B. Phillips, the Co-Editor, G. Cavaliere, and three anonymous referees for very constructive feedback. All remaining errors are ours.

References

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