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Notes And Problems A General Bound For The Limiting Distribution Of Breitung'S Statistic

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  • Davidson, James
  • Magnus, Jan R.
  • Wiegerinck, Jan

Abstract

We consider the Breitung (2002, Journal of Econometrics 108, 343–363) statistic ξn, which provides a nonparametric test of the I(1) hypothesis. If ξ denotes the limit in distribution of ξn as n → ∞, we prove (Theorem 1) that 0 ≤ ξ ≤ 1/π2, a result that holds under any assumption on the underlying random variables. The result is a special case of a more general result (Theorem 3), which we prove using the so-called cotangent method associated with Cauchy's residue theorem.

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  • Davidson, James & Magnus, Jan R. & Wiegerinck, Jan, 2008. "Notes And Problems A General Bound For The Limiting Distribution Of Breitung'S Statistic," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1443-1455, October.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:05:p:1443-1455_08
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    Cited by:

    1. Mehdi Hosseinkouchack, 2014. "Local Asymptotic Power of Breitung's Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 456-462, June.

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