On the asymptotic expansion of the empirical process of long-memory moving averages
长记忆移动平均过程经验过程的渐近展开
Let $X_n = \Sigma_{i=1}^{\infty} a_i \varepsilon_{n-i}$, where the $\varepsilon_i$ are iid with mean 0 finite fourth moment and the $a_i$ are regularly varying with index $-\beta$ where $\beta \epsilon (1/2, 1)$ so that ${X_n}$ has long-range dependence. This covers an important class of the fractional ARIMA process. For $r \geq 0$, let $Y_{N, r} = \sum_{n=1}^N \sum_{1\leq j_1 < \dots < j_r} \Pi_{s=1}^r a_{j_s}, Y_{N, 0} = N, \sigma_{N, r}^2 = \Var(Y_{N, r})$ and $F^{(r)} =$…