Abstract
Let Xn = Σi∞=1 aiε n-i, where the εi are i.i.d, with mean 0 and at least finite second moment, and the ai are assumed to satisfy ai = O(i-β) with β > 1/2. When 1/2 < β < 1, Xn is usually called a long-range dependent or long-memory process. For a certain class of Borel functions K(x1,..., xd+1), d ≥0, from Rd+1 to R, which includes indicator functions and polynomials, the stationary sequence K (Xn, Xn+1,..., Xn+d) is considered. By developing a finite orthogonal expansion of K (Xn,..., Xn+d), the Berry-Esseen type bounds for the normalized sum QN/√N, QN = ε nN=1 (K(Xn,..., Xn+d) - EK(Xn,..., Xn+d)) are obtained when QN/√N obeys the central limit theorem with positive limiting variance.
Original language | English |
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Pages (from-to) | 301-321 |
Number of pages | 21 |
Journal | Bernoulli |
Volume | 14 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2008 May 1 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability