Explosive AR(1) process with independent but not identically distributed errors

Abstract

Anderson (The Annals of Mathematical Statistics 30(3):676-687, 1959) studied the limiting distribution of the least square estimator for explosiveAR(1) process under the independent and identically distributed (iid) condition on error i.e., Xt =.Xt- 1 + et where. > 1 and et is iid error with Ee = 0 and Ee2 < 8. This paper is mainly concerned about the limiting distribution of the least square estimator of., that is.<^>, when errors are not identically distributed. In addition, we provide an approximate description of the limiting distribution of n-1 j=0.- j en- j when. > 1 as n -> infinity.