Representation and Weak Convergence of Stochastic Integrals with Fractional Integrator Processes

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Representation and Weak Convergence of Stochastic Integrals with Fractional Integrator Processes

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James Davidson
Nigar Hashimzade () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

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Abstract

This paper considers the asymptotic distribution of the covariance of a nonstationary frac- tionally 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 rep- resentation, 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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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-45.

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Length: 31
Date of creation: 21 Dec 2007
Date of revision:
Handle: RePEc:aah:create:2007-45

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

NEP-ALL-2008-06-27 (All new papers)
NEP-ECM-2008-06-27 (Econometrics)
NEP-ETS-2008-06-27 (Econometric Time Series)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October. [Downloadable!]
Other versions:
- 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. [Downloadable!]

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