Real-time monitoring with RCA models

TL;DR

This paper introduces weighted CUSUM-based statistics for real-time changepoint detection in Random Coefficient Autoregressive models, applicable to stationary or nonstationary data, with proven asymptotic properties and practical effectiveness.

Contribution

It develops a new family of weighted CUSUM procedures with theoretical guarantees and extends applicability to models with exogenous regressors and nonstationary data.

Findings

Procedures achieve good size control and short detection delays.

Standardising CUSUM improves detection performance.

Method successfully detects changes in epidemiological and housing data.

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.