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Nonstationarity-Extended Whittle Estimation

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  • Shao, Xiaofeng

Abstract

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.

Suggested Citation

  • Shao, Xiaofeng, 2010. "Nonstationarity-Extended Whittle Estimation," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1060-1087, August.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1060-1087_99
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    Citations

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    Cited by:

    1. Artiach, Miguel & Arteche, Josu, 2012. "Doubly fractional models for dynamic heteroscedastic cycles," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2139-2158.
    2. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    3. Peter C. B. Phillips, 2023. "Discrete Fourier Transforms of Fractional Processes with Econometric Applications," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Theory, volume 45, pages 3-71, Emerald Group Publishing Limited.
    4. de Truchis, Gilles, 2013. "Approximate Whittle analysis of fractional cointegration and the stock market synchronization issue," Economic Modelling, Elsevier, vol. 34(C), pages 98-105.
    5. J -P Kreiss & E Paparoditis, 2023. "Bootstrapping Whittle estimators," Biometrika, Biometrika Trust, vol. 110(2), pages 499-518.
    6. Yaya, OlaOluwa S & Gil-Alana, Luis A., 2018. "High and Low Intraday Commodity Prices: A Fractional Integration and Cointegration Approach," MPRA Paper 90518, University Library of Munich, Germany.
    7. Cheung, Ying Lun, 2020. "Nonstationarity-extended Whittle estimation with discontinuity: A correction," Economics Letters, Elsevier, vol. 187(C).
    8. Luis Alberiko Gil-Alana & Tommaso Trani, 2019. "An examination of trade-weighted real exchange rates based on fractional integration," International Economics, CEPII research center, issue 158, pages 64-76.
    9. Ying Lun Cheung & Uwe Hassler, 2020. "Whittle-type estimation under long memory and nonstationarity," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 363-383, September.
    10. Guglielmo Maria Caporale & Luis A. Gil-Alana & Kefei You, 2019. "Stock market linkages between the ASEAN countries, China and the US: a fractional cointegration approach," CESifo Working Paper Series 7537, CESifo.

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