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LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION FOR NONLINEAR PROCESSES

Published online by Cambridge University Press:  14 May 2007

Xiaofeng Shao  and
Wei Biao Wu
Xiaofeng Shao
Affiliation:
University of Illinois at Urbana-Champaign
Wei Biao Wu
Affiliation:
University of Chicago
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Abstract

We study asymptotic properties of the local Whittle estimator of the long memory parameter for a wide class of fractionally integrated nonlinear time series models. In particular, we solve the conjecture posed by Phillips and Shimotsu (2004, Annals of Statistics 32, 656–692) for Type I processes under our framework, which requires a global smoothness condition on the spectral density of the short memory component. The formulation allows the widely used fractional autoregressive integrated moving average (FARIMA) models with generalized autoregressive conditionally heteroskedastic (GARCH) innovations of various forms, and our asymptotic results provide a theoretical justification of the findings in simulations that the local Whittle estimator is robust to conditional heteroskedasticity. Additionally, our conditions are easily verifiable and are satisfied for many nonlinear time series models.We thank Liudas Giraitis for providing the manuscript by Dalla, Giraitis, and Hidalgo (2006). We are grateful to the two referees and the editor for their detailed comments, which led to substantial improvements. We also thank Michael Stein for helpful comments on an earlier version. The work is supported in part by NSF grant DMS-0478704.

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 5 , October 2007 , pp. 899 - 929
Copyright
© 2007 Cambridge University Press

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