监测大流行：COVID-19接触率的分数过滤
Monitoring the pandemic: A fractional filter for the COVID-19 contact rate
摘要：
本文旨在为易感-感染-传播（SIR）模型的COVID-19接触率提供可靠的估计。从确认，恢复和死亡病例的可观察数据中，可以构建接触率的噪声测量。为了滤除测量误差和季节性，建立了一种新的不可观测分量模型。它规定的日志接触率作为一个潜在的，分数积分的过程未知的集成顺序。分数规范反映了聚合社会行为的关键特征，如强持久性和对新信息的逐步调整。一个计算简单的修改卡尔曼滤波器的介绍，并被称为分数滤波器。它允许估计UC模型具有更丰富的长期动态，并提供了一个封闭形式的表达UC模型的预测误差。基于后者，条件平方和（CSS）估计的模型参数的成立是一致的，渐近正态分布。由此得出的几个国家的接触率估计数与大流行的时间顺序完全一致，并可确定政策干预措施产生的不同接触情况。由于分数滤波器显示在样本结束时提供精确的接触率估计，因此它在实时监测大流行方面具有很大的潜力。
英文摘要：
This paper aims to provide reliable estimates for the COVID-19 contact rate of a Susceptible-Infected-Recovered (SIR) model. From observable data on confirmed, recovered, and deceased cases, a noisy measurement for the contact rate can be constructed. To filter out measurement errors and seasonality, a novel unobserved components (UC) model is set up. It specifies the log contact rate as a latent, fractionally integrated process of unknown integration order. The fractional specification reflects key characteristics of aggregate social behavior such as strong persistence and gradual adjustments to new information. A computationally simple modification of the Kalman filter is introduced and is termed the fractional filter. It allows to estimate UC models with richer long-run dynamics, and provides a closed-form expression for the prediction error of UC models. Based on the latter, a conditional-sum-of-squares (CSS) estimator for the model parameters is set up that is shown to be consistent and asymptotically normally distributed. The resulting contact rate estimates for several countries are well in line with the chronology of the pandemic, and allow to identify different contact regimes generated by policy interventions. As the fractional filter is shown to provide precise contact rate estimates at the end of the sample, it bears great potential for monitoring the pandemic in real time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
