Sparse HP Filter: Finding Kinks in the COVID-19 Contact Rate
47 Pages Posted: 9 Jul 2020
Date Written: June 18, 2020
In this paper, we estimate the time-varying COVID-19 contact rate of a Susceptible-Infected-Recovered (SIR) model. Our measurement of the contact rate is constructed using data on actively infected, recovered and deceased cases. We propose a new trend filtering method that is a variant of the Hodrick-Prescott (HP) filter, constrained by the number of possible kinks. We term it the sparse HP filter and apply it to daily data from five countries: Canada, China, South Korea, the UK and the US. Our new method yields the kinks that are well aligned with actual events in each country. We find that the sparse HP filter provides a fewer kinks than the l1 trend filter, while both methods fitting data equally well. Theoretically, we establish risk consistency of both the sparse HP and l1 trend filters. Ultimately, we propose to use time-varying contact growth rates to document and monitor outbreaks of COVID-19.
Note: Funding: This work is in part supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea, the McMaster COVID-19 Research Fund (Stream 2), the European Research Council (ERC-2014-CoG-646917-ROMIA) and the UK Economic and Social Research Council for research grant (ES/P008909/1) to the CeMMAP.
Declaration of Interest: Authors do not have any conflicts of interest.
Keywords: COVID-19, trend filtering, knots, piecewise linear fitting, Hodrick-Prescott filter
JEL Classification: C51, C52, C22
Suggested Citation: Suggested Citation