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This paper aims to provide reliable estimates for the COVID-19 contact rateof a Susceptible-Infected-Recovered (SIR) model. From observable data onconfirmed, recovered, and deceased cases, a noisy measurement for the contactrate can be constructed. To filter out measurement errors and seasonality, anovel unobserved components (UC) model is set up. It specifies the log contactrate as a latent, fractionally integrated process of unknown integration order.The fractional specification reflects key characteristics of aggregate socialbehavior such as strong persistence and gradual adjustments to new information.A computationally simple modification of the Kalman filter is introduced and istermed the fractional filter. It allows to estimate UC models with richerlong-run dynamics, and provides a closed-form expression for the predictionerror 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 andasymptotically normally distributed. The resulting contact rate estimates forseveral countries are well in line with the chronology of the pandemic, andallow to identify different contact regimes generated by policy interventions.As the fractional filter is shown to provide precise contact rate estimates atthe end of the sample, it bears great potential for monitoring the pandemic inreal time.

Monitoring the pandemic: A fractional filter for the COVID-19 contact rate