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Representation and Weak Convergence of Stochastic Integrals with Fractional Integrator Processes

James Davidson () and Nigar Hashimzade

No 807, Discussion Papers from University of Exeter, Department of Economics

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.

Keywords: Stochastic integral; weak convergence; fractional Brownian motion. (search for similar items in EconPapers)
JEL-codes: C22 C32 (search for similar items in EconPapers)
Date: 2008
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http://people.exeter.ac.uk/RePEc/dpapers/DP0807.pdf (application/pdf)

Related works:
Journal Article: REPRESENTATION AND WEAK CONVERGENCE OF STOCHASTIC INTEGRALS WITH FRACTIONAL INTEGRATOR PROCESSES (2009) Downloads
Working Paper: Representation and Weak Convergence of Stochastic Integrals with Fractional Integrator Processes (2007) Downloads
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