On Berry--Esseen bounds for non-instantaneous filters of linear processes

Abstract
Let , where the are i.i.d. with mean 0 and at least finite second moment, and the are assumed to satisfy with . When , is usually called a long-range dependent or long-memory process. For a certain class of Borel functions , , from to , which includes indicator functions and polynomials, the stationary sequence is considered. By developing a finite orthogonal expansion of , the Berry--Esseen type bounds for the normalized sum are obtained when obeys the central limit theorem with positive limiting variance.
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