Degree of predictability of nonlinear autoregressive models

The predictability limits of nonlinear autoregressive (NAR) models applied to processes commonly encountered in experiments are estimated. The process es of interest are random processes, the discrete-time chaotic dynamics of one-dimensional maps, and the continuous-time chaotic dynamics of the Rossl er system. The problem is addressed in terms of maximizing prediction time. Comparison of NAR models with linear autoregressive (LAR) models is conduc ted. For random processes, the prediction time is demonstrated to be compar able with the correlation time. Thus, NAR models only increase the computat ional load over that of the LAR models without noticeably improving the pre diction quality. The same conclusion is drawn for multidimensional continuo us-time chaotic dynamics. For the dynamics of one-dimensional maps, it is d emonstrated that the prediction time may be well above the correlation time and may approach the predictability horizon.