Universal output prediction and nonparametric regression for arbitrary data

We construct a class of elementary nonparametric output predictors of an un known discrete-time nonlinear fading memory system. Our algorithms Predict asymptotically well for every bounded input sequence, every disturbance seq uence in certain classes, and every linear or nonlinear system that is cont inuous and asymptotically time-invariant, causal, and with fading memory. T he predictor is based on k(n)-nearest neighbor estimators from nonparametri c statistics. It uses only previous input and noisy output data of the syst em without any knowledge of the structure of the unknown system, the bounds on the input, or the properties of noise. Under additional smoothness cond itions we provide rates of convergence for the time-average errors of our s cheme. Finally, we apply our results to the special case of stable LTI syst ems.