On extrapolation in some non-linear ar(1) processes

Abstract

A non-linear AR(1) process is investigated in the paper such that its white noise has a rectangular distribution. The process is a direct generalization of the classical linear AR(1) model, to which it can be reduced by a specific choice of a parameter. In the proposed model it is possible to derive explicit formulas for the least squares (LS) extrapolation. It is shown that the LS and the naive extrapolations do not differ too much. This conclusion can be important in applications because there exist models where the difference between the LS and the naive extrapolations can be very large.

Keywords:

• Markov process
• naïve and least squares extrapolations
• non-linear autoregression