Asymptotic Inferences for an AR(1) Model with a Change Point and Possibly Infinite Variance |
| |
| Authors: | Tianxiao Pang Danna Zhang |
| |
| Institution: | 1. Department of MathematicsZhejiang University, Hangzhou, Chinatxpang@zju.edu.cn;3. Department of MathematicsZhejiang University, Hangzhou, China;4. Department of StatisticsUniversity of Chicago, Chicago, Illinois, USA |
| |
| Abstract: | The basic model in this paper is an AR(1) model with a structural break in the AR parameter β at an unknown time k0. That is, yt = β1yt ? 1I{t ? k0} + β2yt ? 1I{t > k0} + ?t, t = 1, 2, ???, T, where I{ · } denotes the indicator function. Suppose |β1| < 1, |β2| < 1, and {?t, t ? 1} is a sequence of i.i.d. random variables which are in the domain of attraction of the normal law with zero mean and possibly infinite variance, then the limiting distributions for the least squares estimators of β1 and β2 are studied in the present paper, which extend some results in Chong (2001 Chong, T.L. (2001). Structural change in AR(1) models. Econometric Theory 17:87–155.Crossref], Web of Science ®] , Google Scholar]). |
| |
| Keywords: | AR(1) model Change point Domain of attraction of the normal law Least squares estimator Limiting distribution |
|
|
