Linear approximations to some non-linear AR(1) processes

summary:Some methods for approximating non-linear AR(1) processes by classical linear AR(1) models are proposed. The quality of approximation is studied in special non-linear AR(1) models by means of comparisons of quality of extrapolation and interpolation in the original models and in their approximations. It is assumed that the white noise has either rectangular or exponential distribution

On geometric ergodicity and prediction in nonnegative non-linear autoregressive processes

summary:A non-linear AR(1) process is investigated when the associated white noise is positive. A criterion is derived for the geometric ergodicity of the process. Some explicit formulas are derived for one and two steps ahead extrapolation. Influence of parameter estimation on extrapolation is studied

Extrapolations in non-linear autoregressive processes

summary:We derive a formula for $m$-step least-squares extrapolation in non-linear AR$(p)$ processes and compare it with the naïve 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