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Representation And Weak Convergence Of Stochastic Integrals With Fractional Integrator Processes

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  • Davidson, James
  • Hashimzade, Nigar

Abstract

This paper considers the asymptotic distribution of the covariance of a nonstationary fractionally integrated process with the stationary increments of another such process - possibly, itself. Questions of interest include the relationship between the harmonic representation of these random variables, which we have analysed in a previous paper, and the construction derived from moving average representations in the time domain. The limiting integrals are shown to be expressible in terms of functionals of Itô integrals with respect to two distinct Brownian motions. Their mean is nonetheless shown to match that of the harmonic representation, and they satisfy the required integration by parts rule. The advantages of our approach over the harmonic analysis include the facts that our formulae are valid for the full range of the long memory parameters, and extend to non-Gaussian processes.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 25 (2009)
Issue (Month): 06 (December)
Pages: 1589-1624

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Handle: RePEc:cup:etheor:v:25:y:2009:i:06:p:1589-1624_99

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  1. Davidson, James & de Jong, Robert M., 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii," Econometric Theory, Cambridge University Press, vol. 16(05), pages 643-666, October.
  2. Davidson, James & Hashimzade, Nigar, 2008. "Alternative Frequency And Time Domain Versions Of Fractional Brownian Motion," Econometric Theory, Cambridge University Press, vol. 24(01), pages 256-293, February.
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Cited by:
  1. Buchmann, Boris & Chan, Ngai Hang, 2013. "Unified asymptotic theory for nearly unstable AR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 952-985.
  2. Christensen, Bent Jesper & Kruse, Robinson & Sibbertsen, Philipp, 2013. "A unified framework for testing in the linear regression model under unknown order of fractional integration," Hannover Economic Papers (HEP) dp-519, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.

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