Nonlinear time series contiguous to AR(1) processes and a related efficient test for linearity

A class of nonlinear time series models contiguous to a first-order autoregressive process (AR(1)) is introduced. The local asymptotic normality of the log-likelihood ratio statistic for testing for linearity is established. An efficient test of linearity is then obtained and its asymptotic power function is derived. An extension to autoregressive conditionally heteroscedastic contiguous alternative models to AR(1) is also discussed and an efficient test of linearity is derived for this class also.