We derive a formula for $m$-step least-squares extrapolation in non-linear AR$(p)$ processes and compare it with the na\"ıve extrapolation. The least-squares extrapolation depends on the distribution of white noise. Some bounds for it are derived that depend only on the expectation of white noise. An example shows that in general case the difference between both types of extrapolation can be very large. Further, a formula for least-squares extrapolation in multidimensional non-linear AR($p$) process is derived.