Sparse HP Filter: Finding Kinks in the COVID-19 Contact Rate

TL;DR

This paper introduces a new sparse HP filter method to identify key change points in COVID-19 contact rates from data, aligning well with real events and offering a clearer understanding of outbreak dynamics.

Contribution

The paper develops a novel sparse HP filter constrained by the number of kinks, improving detection of significant changes in COVID-19 contact rates compared to existing methods.

Findings

Sparse HP filter detects fewer, more meaningful kinks than l1 trend filter.

Both methods fit data equally well, but sparse HP provides clearer change points.

Theoretical risk consistency is established for both filters.

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 $\textit{sparse HP filter}$ 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 $\ell_1$ trend filter, while both methods fitting data equally well. Theoretically, we establish risk consistency of both the sparse HP and $\ell_1$ trend filters. Ultimately, we propose to use time-varying $\textit{contact growth rates}$ to document and monitor outbreaks of COVID-19.