Phase space reconstruction for non-uniformly sampled noisy time series

Area of Science:

• Paleoclimatology
• Dynamical Systems Theory
• Data Analysis

Background:

• Paleoclimate archives (tree rings, lake sediments) provide insights into past climate variability.
• Univariate time series data often require phase space reconstruction for comprehensive analysis.

Purpose of the Study:

• To systematically compare time delay embedding and differential embedding for phase space reconstruction.
• To evaluate the effectiveness of different derivative estimation methods for differential embedding.
• To assess the suitability of these methods for analyzing paleoclimate data.

Main Methods:

• Systematic comparison of time delay embedding and differential embedding.
• Implementation of derivative estimation algorithms: central differences, discrete Legendre coordinates, Moving Taylor Bayesian Regression.
• Evaluation using Lorenz and Rössler systems via recurrence network analysis.
• Application to paleoclimate data from Ecuador and Mexico using windowed recurrence network analysis.

Main Results:

• Differential embedding and time delay embedding performance were evaluated on model systems.
• Recurrence network analysis was used to compare reconstructed and original attractor properties.
• The study identified potential and limitations of phase space reconstruction methods for paleoclimate data.

Conclusions:

• Robustness checks by varying analysis parameters are essential for paleoclimate data interpretation.
• Careful evaluation is needed to determine data suitability for phase space reconstruction and climate variability analysis.