Sparse HP filter: Finding kinks in the COVID-19 contact rate release_dhctizh3tzbhncnratcymyg5we

by Sokbae Lee, Yuan Liao, Myung Hwan Seo, Youngki Shin

Published in Journal of Econometrics by Elsevier BV.

2020  

Abstract

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 <i>sparse HP filter</i> 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 <ns0:math> <ns0:msub><ns0:mrow><ns0:mi>ℓ</ns0:mi></ns0:mrow> <ns0:mrow><ns0:mn>1</ns0:mn></ns0:mrow> </ns0:msub> </ns0:math> trend filter, while both methods fitting data equally well. Theoretically, we establish risk consistency of both the sparse HP and <ns0:math> <ns0:msub><ns0:mrow><ns0:mi>ℓ</ns0:mi></ns0:mrow> <ns0:mrow><ns0:mn>1</ns0:mn></ns0:mrow> </ns0:msub> </ns0:math> trend filters. Ultimately, we propose to use time-varying <i>contact growth rates</i> to document and monitor outbreaks of COVID-19.
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