The sudden onset and quick development of an unknown epidemic may lead to tragic consequences: panic of population due to victims and unpreparedness of authorities for effectively help to population. These circumstances define extremely high requirements to the tools for short-term operational forecast. Namely, such tools should provide reliable results when model of phenomenon is unknown (factors of disease spreading) and data are limited (time series of observations). GMDH-based algorithms just meet these requirements unlike modern differential or advanced statistical models. In this study we test different algorithms from GMDH Shell platform on the example of Covid-19 epidemic in Moscow during the period March 30-April 12, 2020. The forecast horizon is from 1 to 7 days, the initial information is only the official dynamics of diseased patients. Our model is autoregression with variables of different powers. The results of forecast are compared with the accuracy of popular statistical autoregression using exponential smoothing with trend. We suppose that the proposed approach will be useful for short-term forecast at the start of epidemic due to its simplicity and reliability.