This article revisits the asymptotic inference for nonstationary AR(1) models of Phillips and Magdalinos (2007a) by incorporating a structural change in the AR parameter at an unknown time k
0. Consider the model
${y_t} = {\beta _1}{y_{t - 1}}I\{ t \le {k_0}\} + {\beta _2}{y_{t - 1}}I\{ t > {k_0}\} + {\varepsilon _t},t = 1,2, \ldots ,T$
, where I{·} denotes the indicator function, one of
${\beta _1}$
and
${\beta _2}$
depends on the sample size T, and the other is equal to one. We examine four cases: Case (I):
${\beta _1} = {\beta _{1T}} = 1 - c/{k_T}$
,
${\beta _2} = 1$
; (II):
${\beta _1} = 1$
,
${\beta _2} = {\beta _{2T}} = 1 - c/{k_T}$
; (III):
${\beta _1} = 1$
,
${\beta _2} = {\beta _{2T}} = 1 + c/{k_T}$
; and case (IV):
${\beta _1} = {\beta _{1T}} = 1 + c/{k_T}$
,
${\beta _2} = 1$
, where c is a fixed positive constant, and k
T
is a sequence of positive constants increasing to ∞ such that k
T
= o(T). We derive the limiting distributions of the t-ratios of
${\beta _1}$
and
${\beta _2}$
and the least squares estimator of the change point for the cases above under some mild conditions. Monte Carlo simulations are conducted to examine the finite-sample properties of the estimators. Our theoretical findings are supported by the Monte Carlo simulations.