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On Local Trigonometric Regression Under Dependence

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2018

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Ghosh, Sucharita

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https://doi.org/10.1111/jtsa.12287
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Journal of Time Series Analysis. 2018, 39(4), pp. 592-617. ISSN 0143-9782. eISSN 1467-9892. Available under: doi: 10.1111/jtsa.12287

Zusammenfassung

We consider nonparametric estimation of an additive time series decomposition into a long‐term trend μ and a smoothly changing seasonal component S under general assumptions on the dependence structure of the residual process. The rate of convergence of local trigonometric regression estimators of S turns out to be unaffected by the dependence, even though the spectral density of the residual process has a pole at the origin. In contrast, the rate of convergence of nonparametric estimators of μ depends on the long‐memory parameter d. Therefore, in the presence of long‐range dependence, different bandwidths for estimating μ and S should be used. A data adaptive algorithm for optimal bandwidth choice is proposed. Simulations and data examples illustrate the results.

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510 Mathematik

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ISO 690BERAN, Jan, Britta STEFFENS, Sucharita GHOSH, 2018. On Local Trigonometric Regression Under Dependence. In: Journal of Time Series Analysis. 2018, 39(4), pp. 592-617. ISSN 0143-9782. eISSN 1467-9892. Available under: doi: 10.1111/jtsa.12287
BibTex
@article{Beran2018-07Local-42663,
  year={2018},
  doi={10.1111/jtsa.12287},
  title={On Local Trigonometric Regression Under Dependence},
  number={4},
  volume={39},
  issn={0143-9782},
  journal={Journal of Time Series Analysis},
  pages={592--617},
  author={Beran, Jan and Steffens, Britta and Ghosh, Sucharita}
}
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