REPRESENTATION AND WEAK CONVERGENCE OF STOCHASTIC INTEGRALS WITH FRACTIONAL INTEGRATOR PROCESSES

James Davidson and Nigar Hashimzade

Econometric Theory, 2009, vol. 25, issue 06, pages 1589-1624

Abstract: This paper considers the asymptotic distribution of the sample covariance of a nonstationary fractionally integrated process with the stationary increments of another such process -type integrals with respect to distinct Brownian motions. In certain cases the latter terms are of small order relative to the former. The mean is shown to match that of the harmonic representation, where the latter is defined, and satisfies the required integration by parts rule. The advantages of our approach over the harmonic analysis include the facts that our formulas are valid for the full range of the long memory parameters and that they extend to non-Gaussian processes.

Date: 2009

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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:25:y:2009:i:06:p:1589-1624_99

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