A necessary moment condition for the fractional functional central limit theorem (Q2890708)

The authors discuss the moment condition for the fractional functional central limit theorem for partial sums of \(x_t=\Delta^{-d} u_t\) where \(d\) is the fractional integration parameter, \(-{1\over 2}< d<{1\over 2}\) and \(u_t\) is weakly dependent.NEWLINENEWLINE Their main result is to show that when \(-{1\over 2}< d< 0\) and under some relatively weak conditions on \(u_t\), the existence of \(q\geq(d+{1\over 2})^{-1}\) moments is in fact a necessary condition for the fractional functional central limit theorem for fractionally integrated processes and \(q>(d+{1\over 2})^{-1}\) moments are necessary for more general fractional processes.