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NONSTATIONARITY-EXTENDED WHITTLE ESTIMATION

Published online by Cambridge University Press:  04 November 2009

Xiaofeng Shao
Xiaofeng Shao*
Affiliation:
University of Illinois at Urbana-Champaign
*
*Address correspondence to Xiaofeng Shao, Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright St, Champaign, IL, 61820 USA; e-mail: xshao@uiuc.edu
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Abstract

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For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used fractional autoregressive integrated moving average models with generalized autoregressive conditional heteroskedastic-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso, and Giraitis (2007, Journal of Econometrics 141, 1353–1384) and develop the nonstationarity-extended Whittle estimation. The resulting estimator is shown to be asymptotically normal and is more efficient than the tapered Whittle estimator. Finally, the results from a small simulation study are presented to corroborate our theoretical findings.

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Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 4 , August 2010, pp. 1060 - 1087
Copyright
Copyright © Cambridge University Press 2009

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