Wavelet analysis for non-stationary, nonlinear time series
Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysi...
| Main Author: | |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2016-08-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/23/257/2016/npg-23-257-2016.pdf |
| _version_ | 1819097392883957760 |
|---|---|
| author | J. A. Schulte |
| author_facet | J. A. Schulte |
| author_sort | J. A. Schulte |
| collection | DOAJ |
| description | Methods for detecting and quantifying nonlinearities in nonstationary time
series are introduced and developed. In particular, higher-order wavelet
analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO)
time series. Multiple-testing problems inherent in wavelet
analysis were addressed by controlling the false discovery rate. A new local
autobicoherence spectrum facilitated the detection of local nonlinearities
and the quantification of cycle geometry. The local autobicoherence spectrum
of the QBO time series showed that the QBO time series contained a mode with
a period of 28 months that was phase coupled to a harmonic with a period of
14 months. An additional nonlinearly interacting triad was found among modes
with periods of 10, 16 and 26 months. Local biphase spectra determined that the
nonlinear interactions were not quadratic and that the effect of the
nonlinearities was to produce non-smoothly varying oscillations. The
oscillations were found to be skewed so that negative QBO regimes were
preferred, and also asymmetric in the sense that phase transitions between
the easterly and westerly phases occurred more rapidly than those from
westerly to easterly regimes. |
| first_indexed | 2024-12-22T00:14:22Z |
| format | Article |
| id | doaj.art-5c8b3699e30b43a4b1d362e3c778710d |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-12-22T00:14:22Z |
| publishDate | 2016-08-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-5c8b3699e30b43a4b1d362e3c778710d2022-12-21T18:45:21ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462016-08-0123425726710.5194/npg-23-257-2016Wavelet analysis for non-stationary, nonlinear time seriesJ. A. Schulte0The Pennsylvania State University, University Park, Pennsylvania 16802, USAMethods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16 and 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.http://www.nonlin-processes-geophys.net/23/257/2016/npg-23-257-2016.pdf |
| spellingShingle | J. A. Schulte Wavelet analysis for non-stationary, nonlinear time series Nonlinear Processes in Geophysics |
| title | Wavelet analysis for non-stationary, nonlinear time series |
| title_full | Wavelet analysis for non-stationary, nonlinear time series |
| title_fullStr | Wavelet analysis for non-stationary, nonlinear time series |
| title_full_unstemmed | Wavelet analysis for non-stationary, nonlinear time series |
| title_short | Wavelet analysis for non-stationary, nonlinear time series |
| title_sort | wavelet analysis for non stationary nonlinear time series |
| url | http://www.nonlin-processes-geophys.net/23/257/2016/npg-23-257-2016.pdf |
| work_keys_str_mv | AT jaschulte waveletanalysisfornonstationarynonlineartimeseries |