ON THE ASYMPTOTIC EXPANSION OF THE EMPIRICAL PROCESS OF LONG-MEMORY MOVING AVERAGES
ON THE ASYMPTOTIC EXPANSION OF THE EMPIRICAL PROCESS OF LONG-MEMORY MOVING AVERAGES
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DOI：
10.1214/aos/1032526953
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发表时间：
1996-06
影响因子：
4.5
通讯作者：
Hwai-Chung Ho;T. Hsing
中科院分区：
文献类型：
--
作者：
Hwai-Chung Ho;T. Hsing
Let X n = Σ∞ i=1 a i e n-i , where the e i are iid with mean 0 and finite fourth moment and the a i are regularly varying with index -β where β ∈ (1/2,1) so that (X n ) has long-range dependence. This covers an important class of the fractional ARIMA process. For r ≥ 0, let Y N,r = Σ N n=1 Σ 1≤j1<...< jr Π r s=1 a js e n-js , Y N,0 = N, σ2 N,r =Var(Y N,r ) and F (r) = the rth derivative of the distribution function of X n . The Y N,r are uncorrelated and are stochastically decreasing in r. For any positive integer p < (2β - 1) -1 , it is shown under mild regularity conditions that, with probability 1, Σ N n=1 I(X n ≤ x) = Σ p r=0 (-1) r F (r) (x)Y N,r + o(N -λ σN,p) uniformly for all x ∈ R ∀ O < λ < (β - 1/2) Λ (1/2 - p(β - 1/2)). This generalizes a host of existing results and provides the vehicle for a number of statistical applications.
