Asymptotic Inferences for an AR(1) Model with a Change Point: Stationary and Nearly Non-stationary Cases

This paper examines the asymptotic inference for AR(1) models with a possible structural break in the AR parameter β near the unity at an unknown time k₀. Consider the model y_{t}=β₁y_{t-1}I{t≤k₀}+β₂y_{t-1}I{t>k₀}+e_{t}, t=1,2,⋯,T, where I{⋅} denotes the indicator function. We examine two cases: Case (I) |β₁|