The Reduction Principle for the Empirical Process of a Long Memory Linear Process

Liudas Giraitis () and Donatas Surgailis ()
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Liudas Giraitis: London School of Economics, Department of Economics
Donatas Surgailis: Vilnius Institute of Mathematics and Informatics

A chapter in Empirical Process Techniques for Dependent Data, 2002, pp 241-255 from Springer

Abstract: Abstract We discuss the uniform reduction principle for the empirical process of a long memory moving average process X t, t ∈ ℤ with long memory, which generalizes the corresponding reduction principle of Dehling and Taqqu [9]. The proof is based on the expansion of the bivariate probability density t (x 1, x 2) of X 0, X t : $$ {{f}_{1}}({{x}_{1}},{{x}_{2}}) = f({{x}_{1}})f({{x}_{2}}) + {{r}_{t}}f'({{x}_{1}})f'(x2) + o({{r}_{t}}),\quad t \to \infty , $$ uniformly in x 1, x 2, where r t = (X 0, X t ) and f(x) is the marginal probability density. An easy consequence of the reduction principle is the functional CLT for the empirical process. An application of the last result to the change-point problem of the marginal c.d.f. is discussed.

Keywords: Central Limit Theorem; Fractional Brownian Motion; Linear Process; Empirical Process; Gaussian Case (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0099-4_8

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DOI: 10.1007/978-1-4612-0099-4_8

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