Bounds for the least squares extrapolation in non-linear AR(1) processes

It is proved that formula for least squares extrapolation in stationary non-linear AR(1) process is valid also for non-stationary non-linear AR(1) processes. This formula depends on the distribution of the corresponding white noise. If the non-linear function used in the model is non-decreasing and concave, upper and lower bounds are derived for least squares extrapolation such that the bounds depend only on the expectation of the white noise. It is shown in an example that the derived bounds in some cases give a good approximation to the least squares extrapolation.