(1) Structural Change Point Analysis Of The Model Moderate Explosion AR

This paper revisits the asymptotic inference for non-stationary AR(1) model-s of Phillips and Magdalinos (2007) by incorporating a possible structural break in the AR parameter at an unknown time ko-Consider the model yt=β1yt-1I{t≤ko}+β2yt-1I{t>ko}+εt,t=1,2,…,T, where I{·} denotes the indicator function and one of β1and β2depends on the sample size T and the other one is equal to one. We examine two cases:Case (Ⅰ):β1=1,β2=β2T=1+c/kT; and case(Ⅱ):β1=β1T=1+c/kT,β2=1,where c is a fixed positive constant and kT is a sequence of positive constants increasing to oo such that kT=o(T). In addition, suppose{εt,t≥1} is a sequence of i.i.d. random variables which are in the domain of attraction of the normal law with zero means and possibly infinite variances. We derive the limiting distributions of the least squares estimators of β1and β2in this paper. The limiting distribution of the break-point estimator is also discussed for the case (I). An interesting finding is that the convergence rates of the least squares estimators of β1and β2under the situations (Ⅰ) and (Ⅱ), unlike the findings in previous articles(Chong (2001), Pang and Zhang (2013), Pang et al.(2014) and Liang et al.(2014)),are both asymmetric due to the explosive impact of AR parameter1+c/kT.