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On robust local polynomial estimation with long-memory errors

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  • Beran, Jan
  • Feng, Yuanhua
  • Ghosh, Sucharita
  • Sibbertsen, Philipp

Abstract

Prediction in time series models with a trend requires reliable estimation of the trend function at the right end of the observed series. Local polynomial smoothing is a suitable tool because boundary corrections are included implicitly. However, outliers may lead to unreliable estimates, if least squares regression is used. In this paper, local polynomial smoothing based on M-estimation is considered for the case where the error process exhibits long-range dependence. In constrast to the iid case, all M-estimators are asymptotically equivalent to the least square solution, under the (ideal) Gaussian model. Outliers turn out to have a major effect on nonrobust bandwidth selection, in particular due to the change of the dependence structure.
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Suggested Citation

  • Beran, Jan & Feng, Yuanhua & Ghosh, Sucharita & Sibbertsen, Philipp, 2002. "On robust local polynomial estimation with long-memory errors," International Journal of Forecasting, Elsevier, vol. 18(2), pages 227-241.
  • Handle: RePEc:eee:intfor:v:18:y:2002:i:2:p:227-241
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    References listed on IDEAS

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    1. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
    2. Beran, Jan & Ghosh, Sucharita & Sibbertsen, Philipp, 2000. "Nonparametric M-estimation with long-memory errors," Technical Reports 2000,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Jan Beran & Yuanhua Feng, 2002. "Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 291-311, June.
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    Cited by:

    1. Philipp Sibbertsen, 2004. "Long memory versus structural breaks: An overview," Statistical Papers, Springer, vol. 45(4), pages 465-515, October.
    2. Heni Boubaker & Nadia Sghaier, 2014. "Semiparametric Generalized Long Memory Modelling of GCC Stock Market Returns: A Wavelet Approach," Working Papers 2014-66, Department of Research, Ipag Business School.
    3. Jan G. De Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Monash Econometrics and Business Statistics Working Papers 12/05, Monash University, Department of Econometrics and Business Statistics.
    4. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    5. repec:ipg:wpaper:2014-066 is not listed on IDEAS
    6. Beran, Jan & Shumeyko, Yevgen, 2012. "Bootstrap testing for discontinuities under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 322-347.
    7. Boubaker, Heni & Sghaier, Nadia, 2015. "Semiparametric generalized long-memory modeling of some mena stock market returns: A wavelet approach," Economic Modelling, Elsevier, vol. 50(C), pages 254-265.

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