In this study, the correlation sum and the correlation integral for chaotic time series using the Supremum norm and the Euclidean norm are discussed. The correlation integrals are then used to develop governing equations for the correlation sum, noise level and correlation dimension in which the correlation dimension and the noise level are linearly dependent on each other. Some linear estimation methods for the noise level are then introduced by using these equations. The estimation methods are applied to four chaotic time series (two artificial and two real-world). By comparing the performances of the estimations of the noise level, the best estimating method is then suggested. Copyright © 2012 World Scientific Publishing Company.
CitationXu, P., Li, W. K., & Jayawardena, A. W. (2012). Noise level estimation for a chaotic time series. International Journal of Bifurcation and Chaos, 22(3). Retrieved from https://doi.org/10.1142/S0218127412500526
- Chaotic time series
- Noise level
- Correlation integral