A general bound for the limiting distribution of Breitung's statistic
Magnus, Jan R.
University of Exeter; Tilburg University; University of Amsterdam
Cambridge University Press
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.
Author's draft, December 21, 2007
Econometric Theory (2008), 24:1443-1455