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Type of Publication: | Journal article |
Publication status: | Published |
Author: | Beran, Jan; Steffens, Britta; Ghosh, Sucharita |
Year of publication: | 2018 |
Published in: | Journal of Time Series Analysis ; 39 (2018), 4. - pp. 592-617. - ISSN 0143-9782. - eISSN 1467-9892 |
DOI (citable link): | https://dx.doi.org/10.1111/jtsa.12287 |
Summary: |
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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Subject (DDC): | 510 Mathematics |
Bibliography of Konstanz: | Yes |
Refereed: | Yes |
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BERAN, Jan, Britta STEFFENS, Sucharita GHOSH, 2018. On Local Trigonometric Regression Under Dependence. In: Journal of Time Series Analysis. 39(4), pp. 592-617. ISSN 0143-9782. eISSN 1467-9892. Available under: doi: 10.1111/jtsa.12287
@article{Beran2018-07Local-42663, title={On Local Trigonometric Regression Under Dependence}, year={2018}, doi={10.1111/jtsa.12287}, 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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