On the order of magnitude of sums of negative powers of integrated processes (Q2845026)

The asymptotic behaviour of expressions of the form \(\sum_{i=1}^n f(r_nx_t)\), where \(x_t\) is an integrated process, \(r_n\) is a sequence of norming constants, and \(f\) is measurable, has been the subject of several articles in recent years. In this paper upper and lower bounds on the order of magnitude of \(\sum_{i=1}^n |x_t|^{-\alpha}\), where \(x_t\) is an integrated process, are obtained. Moreover, upper bounds for the order of magnitude of the related quantity \(\sum_{i=1}^n v_t|x_t|^{-\alpha}\), where \(v_t\) are random variables satisfying certain conditions, are also derived.