G-Filtering Nonstationary Time Series
The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series,...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2012/738636 |
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| _version_ | 1832556992427720704 |
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| author | Mengyuan Xu Krista B. Cohlmia Wayne A. Woodward Henry L. Gray |
| author_facet | Mengyuan Xu Krista B. Cohlmia Wayne A. Woodward Henry L. Gray |
| author_sort | Mengyuan Xu |
| collection | DOAJ |
| description | The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series, the TVF components often overlap in time. In such a situation, the classical linear filtering method fails to extract components from the original process. In this paper, we introduce and theoretically develop the G-filter based on a time-deformation technique. Simulation examples and a real bat echolocation example illustrate that the G-filter can successfully filter a G-stationary process whose TVF components overlap with time. |
| format | Article |
| id | doaj-art-ef411caf968748ccb5ddfb3a455a51d8 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-ef411caf968748ccb5ddfb3a455a51d82025-02-03T05:44:04ZengWileyJournal of Probability and Statistics1687-952X1687-95382012-01-01201210.1155/2012/738636738636G-Filtering Nonstationary Time SeriesMengyuan Xu0Krista B. Cohlmia1Wayne A. Woodward2Henry L. Gray3Biostatistics Branch, NIH/NIEHS (National Institutes of Health/National Institute of Environmental Health Sciences), Research Triangle Park, NC 27709, USADepartment of Mathematics, Odessa College, Odessa, TX 79764, USADepartment of Statistical Science, Southern Methodist University, Dallas, TX 75205, USADepartment of Statistical Science, Southern Methodist University, Dallas, TX 75205, USAThe classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series, the TVF components often overlap in time. In such a situation, the classical linear filtering method fails to extract components from the original process. In this paper, we introduce and theoretically develop the G-filter based on a time-deformation technique. Simulation examples and a real bat echolocation example illustrate that the G-filter can successfully filter a G-stationary process whose TVF components overlap with time.http://dx.doi.org/10.1155/2012/738636 |
| spellingShingle | Mengyuan Xu Krista B. Cohlmia Wayne A. Woodward Henry L. Gray G-Filtering Nonstationary Time Series Journal of Probability and Statistics |
| title | G-Filtering Nonstationary Time Series |
| title_full | G-Filtering Nonstationary Time Series |
| title_fullStr | G-Filtering Nonstationary Time Series |
| title_full_unstemmed | G-Filtering Nonstationary Time Series |
| title_short | G-Filtering Nonstationary Time Series |
| title_sort | g filtering nonstationary time series |
| url | http://dx.doi.org/10.1155/2012/738636 |
| work_keys_str_mv | AT mengyuanxu gfilteringnonstationarytimeseries AT kristabcohlmia gfilteringnonstationarytimeseries AT wayneawoodward gfilteringnonstationarytimeseries AT henrylgray gfilteringnonstationarytimeseries |