Abstract: In non-linear autoregressive models, minimum variance multi-step ahead predictors involve knowledge of both the system parameters and the probability distribution of the unobservable random disturbances. Herein we study adaptive versions of these optimal predictors when neither the system parameters nor the underlying error distribution are known in advance and have to be estimated from the data. Under certain assumptions, we show that the cumulative squared differencebetween the optimal predictors and their adaptive versions is of the order of log n, generalizing previous results on least squares adaptive prediction in linear stochastic systems.
Key words and phrases: Linear and non-linear ARX models, adaptive prediction, strong consistency, linear and non-linear stochastic regression.