Limit theory for explosive autoregression under conditional heteroskedasticity

This paper studies an explosive autoregression with conditionally heteroskedastic innovations. The asymptotic distributions of LS, GLS, t-statistics, heteroskedasticity-consistent t-statistics and GLS t-statistics are derived for nonstationary local-to-unity and mildly explosive roots, in which ρn satisfies n1−ρn→−∞,0. Combined with the existing results, we can cover the range of ρn such that n1−ρn→−∞,∞. Some results on pure explosive cases are also discussed.