NOTES AND PROBLEMS A GENERAL BOUND FOR THE LIMITING DISTRIBUTION OF BREITUNGʹS STATISTIC

We consider the Breitung ~2002, Journal of Econometrics 108, 343–363! statistic jn, which provides a nonparametric test of the I~1! hypothesis+ If j denotes the limit in distribution of jn as n r `, we prove ~Theorem 1! that 0 j 10p2, 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+