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On estimation of mean and covariance functions in repeated time series with long-memory errors

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2014

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https://doi.org/10.1007/s10986-014-9224-1
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Lithuanian Mathematical Journal. 2014, 54(1), pp. 8-34. ISSN 0363-1672. eISSN 1573-8825. Available under: doi: 10.1007/s10986-014-9224-1

Zusammenfassung

We consider kernel estimation of trend and covariance functions in models typically encountered in functional data analysis (FDA), with the modification that the random curves are perturbed by error processes that exhibit short- or long-range dependence. Uniform convergence of standardized maximal differences between estimated and true (trend and covariance) functions is established. For the covariance function, a transformation based on contrasts is proposed that does not require explicit trend estimation. Improved estimators can be obtained by using higher-order kernels.

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510 Mathematik

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long-range dependence, kernel estimation, repeated time series, covariance function, higher-order kernels, functional limit theorem

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ISO 690BERAN, Jan, Haiyan LIU, 2014. On estimation of mean and covariance functions in repeated time series with long-memory errors. In: Lithuanian Mathematical Journal. 2014, 54(1), pp. 8-34. ISSN 0363-1672. eISSN 1573-8825. Available under: doi: 10.1007/s10986-014-9224-1
BibTex
@article{Beran2014estim-29159,
  year={2014},
  doi={10.1007/s10986-014-9224-1},
  title={On estimation of mean and covariance functions in repeated time series with long-memory errors},
  number={1},
  volume={54},
  issn={0363-1672},
  journal={Lithuanian Mathematical Journal},
  pages={8--34},
  author={Beran, Jan and Liu, Haiyan}
}
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