TITLE:
Selection of Optimal Embedding Parameters Applied to Short and Noisy Time Series from Rössler System
AUTHORS:
Olivier Delage, Alain Bourdier
KEYWORDS:
Phase Space Reconstruction, Embedding Window, Rössler System, Time Series, Correlation Integral, Delay Time
JOURNAL NAME:
Journal of Modern Physics,
Vol.8 No.9,
August
31,
2017
ABSTRACT: Throughout scientific research, the state space reconstruction that embeds a non-linear time series is the first and necessary step for characterizing and predicting the behavior of a complex system. This requires to choose appropriate values of time delay T and embedding dimension dE. Three methods are applied and discussed on nonlinear time series provided by the Rössler attractor equations set: Cao’s method, the C-C method developed by Kim et al. and the C-C-1 method developed by Cai et al. A way to fix a parameter necessary to implement the last method is given. Focus has been put on small size and/or noisy time series. The reconstruction quality is measured by using a criterion based on the transformation smoothness.