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Simple noise-reduction method based on nonlinear forecasting.

James P L Tan¹

¹Interdisciplinary Graduate School, Nanyang Technological University, Singapore and Complexity Institute, Nanyang Technological University, Singapore.

Physical Review. E

|April 19, 2017

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This study introduces an objective, multivariate noise reduction method for time series data, improving upon existing techniques by using nonlinear forecasting to overcome limitations in parameter selection and enhance accuracy in complex datasets.

Area of Science:

* Time Series Analysis
* Nonlinear Dynamics
* Signal Processing

Background:

* Conventional noise reduction methods for time series data often rely on subjective parameter choices.
* Existing methods struggle when no satisfactory models exist to fit the data.
* State-space reconstruction provides a theoretical basis for nonparametric forecasting.

Purpose of the Study:

* To present a novel, objective multivariate noise reduction method.
* To improve upon existing noise reduction techniques, specifically Schreiber's method.
* To demonstrate the effectiveness of nonlinear forecasting in optimizing noise reduction.

Main Methods:

* Developed a multivariate noise reduction technique utilizing nonlinear forecasting.

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* Employed state-space reconstruction as the foundation for the forecasting models.

* Addressed a flaw in Schreiber's method by incorporating forecasting.

* Extended the method for application to multivariate time series.

Main Results:

* The proposed method successfully reduced noise in multivariate time series.
* Demonstrated objective optimization of noise reduction heuristics using in-sample forecasting errors.
* Showcased the method's efficacy on diverse datasets, including the Van der Pol oscillator, Lorenz equations, and Hindmarsh-Rose model.
* Validated the correlation between in-sample forecasting errors and actual noise reduction performance.

Conclusions:

* The presented method offers an objective and effective approach to multivariate time series noise reduction.
* Nonlinear forecasting provides a robust mechanism for optimizing noise reduction parameters.
* The technique overcomes limitations of previous methods and is applicable to complex dynamical systems and real-world data.