Spline Autoregression Method for Estimation of Quantile Spectrum
<p>Based on trigonometric quantile regression, the quantile spectrum was introduced in Li (<a href="#CIT0024" target="_blank">2008</a>, <a href="#CIT0025" target="_blank">2012</a>) as an alternative tool for spectral analysis of t...
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2025
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| _version_ | 1852015520477347840 |
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| author | Ta-Hsin Li (15236771) |
| author_facet | Ta-Hsin Li (15236771) |
| author_role | author |
| dc.creator.none.fl_str_mv | Ta-Hsin Li (15236771) |
| dc.date.none.fl_str_mv | 2025-10-24T20:20:18Z |
| dc.identifier.none.fl_str_mv | 10.6084/m9.figshare.29963491.v2 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/dataset/Spline_Autoregression_Method_for_Estimation_of_Quantile_Spectrum/29963491 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Medicine Genetics Ecology Inorganic Chemistry Environmental Sciences not elsewhere classified Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Fourier transform Penalized least-squares Periodogram Quantile-frequency analysis Quantile regression Quantile series Spectral analysis Spline Time series |
| dc.title.none.fl_str_mv | Spline Autoregression Method for Estimation of Quantile Spectrum |
| dc.type.none.fl_str_mv | Dataset info:eu-repo/semantics/publishedVersion dataset |
| description | <p>Based on trigonometric quantile regression, the quantile spectrum was introduced in Li (<a href="#CIT0024" target="_blank">2008</a>, <a href="#CIT0025" target="_blank">2012</a>) as an alternative tool for spectral analysis of time series. It has been demonstrated to have the capability of providing a richer view of time series data than that offered by the ordinary spectrum especially for nonlinear dynamics such as stochastic volatility. A novel method, called spline autoregression (SAR), is proposed in this article for estimating the quantile spectrum as a bivariate function of frequency and quantile level, under the assumption that the quantile spectrum varies smoothly with the quantile level. The SAR method is facilitated by the quantile discrete Fourier transform (QDFT) based on trigonometric quantile regression. It is enabled by the resulting time-domain quantile series (QSER) which represents properly scaled oscillatory characteristics of the original time series around a quantile. A functional autoregressive model is fitted to the QSER on a grid of quantile levels by penalized least-squares, where the autoregressive coefficients are represented as spline functions of the quantile level. While the ordinary autoregressive (AR) model is widely used for conventional spectral estimation, the simulation study in this article confirms that the proposed SAR method provides an effective way of estimating the quantile spectrum as a bivariate function in comparison with the alternatives. Supplementary materials for this article are available online.</p> |
| eu_rights_str_mv | openAccess |
| id | Manara_c4e1310244b5d3a67ec6ce34e68d562e |
| identifier_str_mv | 10.6084/m9.figshare.29963491.v2 |
| network_acronym_str | Manara |
| network_name_str | ManaraRepo |
| oai_identifier_str | oai:figshare.com:article/29963491 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Spline Autoregression Method for Estimation of Quantile SpectrumTa-Hsin Li (15236771)MedicineGeneticsEcologyInorganic ChemistryEnvironmental Sciences not elsewhere classifiedBiological Sciences not elsewhere classifiedMathematical Sciences not elsewhere classifiedFourier transformPenalized least-squaresPeriodogramQuantile-frequency analysisQuantile regressionQuantile seriesSpectral analysisSplineTime series<p>Based on trigonometric quantile regression, the quantile spectrum was introduced in Li (<a href="#CIT0024" target="_blank">2008</a>, <a href="#CIT0025" target="_blank">2012</a>) as an alternative tool for spectral analysis of time series. It has been demonstrated to have the capability of providing a richer view of time series data than that offered by the ordinary spectrum especially for nonlinear dynamics such as stochastic volatility. A novel method, called spline autoregression (SAR), is proposed in this article for estimating the quantile spectrum as a bivariate function of frequency and quantile level, under the assumption that the quantile spectrum varies smoothly with the quantile level. The SAR method is facilitated by the quantile discrete Fourier transform (QDFT) based on trigonometric quantile regression. It is enabled by the resulting time-domain quantile series (QSER) which represents properly scaled oscillatory characteristics of the original time series around a quantile. A functional autoregressive model is fitted to the QSER on a grid of quantile levels by penalized least-squares, where the autoregressive coefficients are represented as spline functions of the quantile level. While the ordinary autoregressive (AR) model is widely used for conventional spectral estimation, the simulation study in this article confirms that the proposed SAR method provides an effective way of estimating the quantile spectrum as a bivariate function in comparison with the alternatives. Supplementary materials for this article are available online.</p>2025-10-24T20:20:18ZDatasetinfo:eu-repo/semantics/publishedVersiondataset10.6084/m9.figshare.29963491.v2https://figshare.com/articles/dataset/Spline_Autoregression_Method_for_Estimation_of_Quantile_Spectrum/29963491CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/299634912025-10-24T20:20:18Z |
| spellingShingle | Spline Autoregression Method for Estimation of Quantile Spectrum Ta-Hsin Li (15236771) Medicine Genetics Ecology Inorganic Chemistry Environmental Sciences not elsewhere classified Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Fourier transform Penalized least-squares Periodogram Quantile-frequency analysis Quantile regression Quantile series Spectral analysis Spline Time series |
| status_str | publishedVersion |
| title | Spline Autoregression Method for Estimation of Quantile Spectrum |
| title_full | Spline Autoregression Method for Estimation of Quantile Spectrum |
| title_fullStr | Spline Autoregression Method for Estimation of Quantile Spectrum |
| title_full_unstemmed | Spline Autoregression Method for Estimation of Quantile Spectrum |
| title_short | Spline Autoregression Method for Estimation of Quantile Spectrum |
| title_sort | Spline Autoregression Method for Estimation of Quantile Spectrum |
| topic | Medicine Genetics Ecology Inorganic Chemistry Environmental Sciences not elsewhere classified Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Fourier transform Penalized least-squares Periodogram Quantile-frequency analysis Quantile regression Quantile series Spectral analysis Spline Time series |