  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.
