论文标题
稀疏的HP滤波器：在Covid-19接触率中找到扭结
Sparse HP Filter: Finding Kinks in the COVID-19 Contact Rate
论文作者
论文摘要
在本文中，我们估计了易感感染的（SIR）模型的随时间变化的COVID-19的接触率。我们对接触率的测量是使用主动感染，恢复和死亡病例的数据来构建的。我们提出了一种新的趋势过滤方法，该方法是Hodrick-Prescott（HP）滤波器的变体，受到可能的扭结数量的约束。我们将其称为$ \ textit {稀疏的HP Filter} $，并将其应用于来自五个国家 /地区的每日数据：加拿大，中国，韩国，英国和美国。我们的新方法产生的扭结与每个国家的实际事件都很好。我们发现，稀疏的HP过滤器提供的扭结比$ \ ell_1 $趋势过滤器少，而两种方法都符合数据的拟合。从理论上讲，我们建立了稀疏HP和$ \ ell_1 $趋势过滤器的风险一致性。最终，我们建议使用时间变化的$ \ textit {联系人增长率} $来记录和监视Covid-19的爆发。
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.
