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Limit theory for explosive autoregression under conditional heteroskedasticity

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Abstract 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… Click to show full abstract

Abstract 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 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.

Keywords: theory explosive; autoregression; autoregression conditional; heteroskedasticity; limit theory; explosive autoregression

Journal Title: Journal of Statistical Planning and Inference
Year Published: 2017

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