This paper extends the canonical model of epidemiology, the SIRD model, to allow for time-varying parameters for real-time measurement and prediction of the trajectory of the Covid-19 pandemic. Time variation in model parameters is captured using the generalized autoregressive score modeling structure designed for the typical daily count data related to the pandemic. The resulting specification permits a flexible yet parsimonious model with a low computational cost. The model is extended to allow for unreported cases as well. Results suggest that these cases' effects on the parameter estimates diminish with the increasing number of testing. Full sample results show that the flexible framework captures the successive waves of the pandemic accurately. A real-time exercise indicates that the proposed structure delivers timely and precise information on the pandemic's current stance. This superior performance, in turn, transforms into accurate predictions of the confirmed cases.