Simple noise-reduction method based on nonlinear forecasting
Nonparametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional noise reduction methods depend on subjective choices of smoothing parameters. Here we present a simple multivariat...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/87351 http://hdl.handle.net/10220/44451 |
| _version_ | 1811693718072197120 |
|---|---|
| author | Tan, James Peng Lung |
| author2 | Interdisciplinary Graduate School (IGS) |
| author_facet | Interdisciplinary Graduate School (IGS) Tan, James Peng Lung |
| author_sort | Tan, James Peng Lung |
| collection | NTU |
| description | Nonparametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional noise reduction methods depend on subjective choices of smoothing parameters. Here we present a simple multivariate noise reduction method based on available nonlinear forecasting techniques. These are in turn based on state-space reconstruction for which a strong theoretical justification exists for their use in nonparametric forecasting. The noise reduction method presented here is conceptually similar to Schreiber's noise reduction method using state-space reconstruction. However, we show that Schreiber's method has a minor flaw that can be overcome with forecasting. Furthermore, our method contains a simple but nontrivial extension to multivariate time series. We apply the method to multivariate time series generated from the Van der Pol oscillator, the Lorenz equations, the Hindmarsh-Rose model of neuronal spiking activity, and to two other univariate real-world data sets. It is demonstrated that noise reduction heuristics can be objectively optimized with in-sample forecasting errors that correlate well with actual noise reduction errors. |
| first_indexed | 2024-10-01T06:56:08Z |
| format | Journal Article |
| id | ntu-10356/87351 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:56:08Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/873512020-11-01T04:45:27Z Simple noise-reduction method based on nonlinear forecasting Tan, James Peng Lung Interdisciplinary Graduate School (IGS) Complexity Institute Forecasting Error Multivariate Time Series Nonparametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional noise reduction methods depend on subjective choices of smoothing parameters. Here we present a simple multivariate noise reduction method based on available nonlinear forecasting techniques. These are in turn based on state-space reconstruction for which a strong theoretical justification exists for their use in nonparametric forecasting. The noise reduction method presented here is conceptually similar to Schreiber's noise reduction method using state-space reconstruction. However, we show that Schreiber's method has a minor flaw that can be overcome with forecasting. Furthermore, our method contains a simple but nontrivial extension to multivariate time series. We apply the method to multivariate time series generated from the Van der Pol oscillator, the Lorenz equations, the Hindmarsh-Rose model of neuronal spiking activity, and to two other univariate real-world data sets. It is demonstrated that noise reduction heuristics can be objectively optimized with in-sample forecasting errors that correlate well with actual noise reduction errors. Published version 2018-02-26T04:43:48Z 2019-12-06T16:40:05Z 2018-02-26T04:43:48Z 2019-12-06T16:40:05Z 2017 Journal Article Tan, J. P. L. (2017). Simple noise-reduction method based on nonlinear forecasting. Physical Review E, 95(3), 032218-. 1539-3755 https://hdl.handle.net/10356/87351 http://hdl.handle.net/10220/44451 10.1103/PhysRevE.95.032218 en Physical Review E © 2017 American Physical Society (APS). This paper was published in Physical Review E and is made available as an electronic reprint (preprint) with permission of American Physical Society (APS). The published version is available at: [http://dx.doi.org/10.1103/PhysRevE.95.032218]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 6 p. application/pdf |
| spellingShingle | Forecasting Error Multivariate Time Series Tan, James Peng Lung Simple noise-reduction method based on nonlinear forecasting |
| title | Simple noise-reduction method based on nonlinear forecasting |
| title_full | Simple noise-reduction method based on nonlinear forecasting |
| title_fullStr | Simple noise-reduction method based on nonlinear forecasting |
| title_full_unstemmed | Simple noise-reduction method based on nonlinear forecasting |
| title_short | Simple noise-reduction method based on nonlinear forecasting |
| title_sort | simple noise reduction method based on nonlinear forecasting |
| topic | Forecasting Error Multivariate Time Series |
| url | https://hdl.handle.net/10356/87351 http://hdl.handle.net/10220/44451 |
| work_keys_str_mv | AT tanjamespenglung simplenoisereductionmethodbasedonnonlinearforecasting |