The North Atlantic Oscillation (NAO) has a significant impact on seasonal climate and surface weather conditions throughout Europe, North America and the North Atlantic. In this paper, we study a number of linear and nonlinear models for a station-based time series of the daily winter NAO. We find that a class of nonlinear models, including both short and long lags, excellently reproduce the characteristic statistical properties of the NAO. These models can hence be used to simulate the NAO.