There exist two major mechanisms which are responsible for the fading phenomenon at HF frequencies. They are the multiple-mode interference and distortions due to the ionospheric irregularities. Fading time series produced by the first of these mechanisms alone should typically represent a multiple-periodical process. This kind of signal may also be produced by an autonomous dynamical system. The character of the time series produced by the second mechanism depends on the nature of the ionospheric irregularities. Recently, evidence has been accumulated to show that sometimes the ionospheric turbulence on equatorial and middle latitudes represents a low-dimensional deterministic chaotic process. These facts suggest that for both mechanisms the fading time series may have a deterministic nature and therefore is predictable. Accordingly we apply the nonlinear predicting technique proposed by Farmer and Sidorovich  to the fading time series obtained by the University of Illinois HF sounder. In its application the prediction technique is modified to take into account specifics of the HF data. For comparison, the conventional linear autoregression prediction technique is also tested. It is found that, in general, the nonlinear prediction and the linear autoregressive forecasting allow prediction on a few correlation times and work with roughly the same success.