Severe geomagnetic disturbances can be hazardous for modern technological systems. The reliable forecast of parameters related to the state of the magnetosphere can facilitate the mitigation of adverse effects of space weather. This study is devoted to the modeling and forecasting of the evolution of the Kp index related to global geomagnetic disturbances. Throughout this work the Nonlinear AutoRegressive with eXogenous inputs (NARX) methodology is applied. Two approaches are presented: i) a recursive sliding window approach, and ii) a direct approach. These two approaches are studied separately and are then compared to evaluate their performances. It is shown that the direct approach outperforms the recursive approach, but both tend to produce predictions slightly biased from the true values for low and high disturbances.