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ALTERNATIVE FREQUENCY AND TIME DOMAIN VERSIONS OF FRACTIONAL BROWNIAN MOTION

Published online by Cambridge University Press:  06 September 2007

James Davidson  and
Nigar Hashimzade
James Davidson
Affiliation:
University of Exeter
Nigar Hashimzade
Affiliation:
University of Exeter
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Abstract

This paper compares models of fractional processes and associated weak convergence results based on moving average representations in the time domain with spectral representations. Both approaches have been applied in the literature on fractional processes. We point out that the conventional forms of these models are not equivalent, as is commonly assumed, even under a Gaussianity assumption. We show that it is necessary to distinguish between “two-sided” processes depending on both leads and lags from one-sided or “causal” processes, because in the case of fractional processes these models yield different limiting properties. We derive new representations of fractional Brownian motion and show how different results are obtained for, in particular, the distribution of stochastic integrals in the multivariate context. Our results have implications for valid statistical inference in fractional integration and cointegration models.We thank F. Hashimzade and two anonymous referees for their valuable comments.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 1 , February 2008 , pp. 256 - 293
Copyright
© 2008 Cambridge University Press

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