key: cord-0884822-rqibzivu
authors: Kim, Young-Joo; Seo, Myung Hwan; Yeom, Hyun-E
title: Discussion on selecting the number of breaks in the pattern of spread of COVID-19 (a reply to Zhao and Liang)
date: 2020-08-28
journal: Int J Infect Dis
DOI: 10.1016/j.ijid.2020.08.064
sha: 8f70f6fe4008b5c91e92336e7fde04f8227016e0
doc_id: 884822
cord_uid: rqibzivu

nan

letter proposes an approach to apply the AIC. To that end, it proposes a continuously time-varying parameter model where the variation of the parameter follows a linear time trend with kinks. Under an additional parametric assumption on the multiplicative noise (a Gamma process), the authors estimate the number of kinks based on the AIC. We discuss a few issues with their comments.

First is an issue related to the data. The transmission rate in the baseline SIR model captures the rate of change in the number of infected, not that of the newly infected. However, they employed the number of the newly infected to estimate the parameters, which invalidates their claim about the number of kinks at the transmission parameter in the SIR model.

Second is an issue on the statistical methodology. Specifically, the penalty term embedded in the AIC criterion may need to be justified more carefully. For instance, Ng and Perron (2001) highlighted the importance of adjusting the magnitude of the penalty according to the time series property of the data in the context of the lag length selection for the unit root testing. Since Zhao and Liang (2020) propose a model with a nonlinear time trend, the time series is not stationary and thus some concerns noted by Ng and Perron (2011) may occur. In this vein, we recommend the letter's authors and readers to refer to the work by Lee et al. (2020) . They propose various ways to fit the time-varying transmission rate by the linear time trend with kinks, as in the Zhao and Liang (2020) , through several different regularization methods and relates them to the well-known HP-filtering in the time series literature. They also provide certain statistical guarantee.

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