In this paper,,ve consider using a semiparametric regression approach
to modelling non-linear autoregressive time series. Based on a finite
series approximation to non-parametric components, an adaptive selecti
on procedure for the number of summands Tn the series approximation is
proposed. Meanwhile, a large sample study is detailed and a small sam
ple simulation for the Maekey-Glass system is presented to support the
large sample study.