The effects of irregular sampling and missing data on largest Lyapunov exponents

Area of Science:

• Dynamical Systems
• Time Series Analysis
• Computational Neuroscience

Background:

• Human self-report data often exhibit irregular sampling rates.
• Calculating the largest Lyapunov exponent (λ1), a chaos indicator, is difficult with such data.

Purpose of the Study:

• To assess methods for calculating λ1 from irregularly sampled time series data.
• To determine the impact of missing data and patching techniques on λ1 estimation.

Main Methods:

• Synthetic time series data were generated and subjected to data point removal (uniform random or power law).
• Missing data segments were patched using segment concatenation, average filling, or local phase space interpolation.
• λ1 was calculated for complete and patched datasets.

Main Results:

• Accurate λ1 estimation is possible with up to 15-20% missing data, depending on the system and patching method.
• Segment concatenation proved robust for self-similar data.
• Local phase space interpolation was effective but required substantial intact data.

Conclusions:

• Effective strategies exist for estimating λ1 from irregularly sampled time series.
• Data patching techniques, particularly segment concatenation, can preserve chaos dynamics.
• Careful consideration of data loss and patching methods is crucial for reliable λ1 calculation.