Holderian functional central limit theorem for linear processes
Let (Xt)t ≥ 1 be a linear process defined by Xt = ∑i=0∞ψi εt-1 where (ψi, i ≥ 0) is a sequence of real numbers and (εi , i ∈ Z) is a sequence of random variables with null expectation and variance 1. This paper provides Hölderian FCLT for (Xt)t ≥ 1 with wide class of filters. Filters with ψ(i)...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2004-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/32281 |
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| Summary: | Let (Xt)t ≥ 1 be a linear process defined by Xt = ∑i=0∞ψi εt-1 where (ψi, i ≥ 0) is a sequence of real numbers and (εi , i ∈ Z) is a sequence of random variables with null expectation and variance 1. This paper provides Hölderian FCLT for (Xt)t ≥ 1 with wide class of filters. Filters with ψ(i) = l(i)/i for a slowly varying function l(i) are allowed. The weak convergence of polygonal line process build from sums of (Xt)t ≥ 1 to the standard Brownian motion W in the Hölder space (Hα), 0 < α < 1/2 - 1/τ holds provided the proper noise behavior is satisfied: E|ε1|τ < ∞, τ > 2.
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| ISSN: | 0132-2818 2335-898X |