On Multi-Step Non-Linear Least Squares Prediction

We first observe that the conditional variance of the error of an m-step non-linear leastsquares predictor is not necessarily a monotonic non-decreasing function of m. This fact has not been documented to the best of our knowledge. We have also studied methods of evaluating the conditional variance for non-linear autoregressive models and illustrated these with both real and simulated data. Bias correction is included. The facility afforded by Chapman-Kolmogorov's equation is highlighted. The possible role played by the skeleton is mentioned briefly. Moreover, the possibility of combinations of forecasts is explored, partly with a view to obtaining robust forecast against prospective influential data.