Limit Theory for Explosive Autoregression Under Conditional Heteroskedasticity

Abstract

This paper studies an explosive autoregression with conditionally heteroskedastic innovations. The asymptotic distributions of LS, GLS, t-statitiscs, heteroskedasticity-consistent t-statistics and GLS t-statistics are derived for nonstationary local-to-unity and mildly explosive roots, in which ρ_{n} satisfies n(1-ρ_{n})→[-∞,0). Combined with the existing results, we can cover the range of ρ_{n} such that n(1-ρ_{n})→[-∞,∞]. Some results on pure explosive cases are also discussed.