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Local Whittle estimation of fractional integration for nonlinear processes. Econometric Theory

By Xiaofeng Shao and Wei Biao Wu


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 FARIMA models with 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.

Year: 2006
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