David M. Kreindler, University of Toronto
Charles J. Lumsden, University of Toronto

Abstract: Human self-report time series data are typically marked by irregularities in sampling rates arising from the data generation process. The largest Lyapunov exponent lamda_1 is an indicator of chaos in time series data. Relatively little has been published to assist the calculation of lamda_1's using irregularly sampled data. We report the results of a series of computational experiments on synthetic data sets assessing techniques for handling irregular time series data in the calculation of lamda_1 . Regularly sampled data sets were disrupted by data point removal using an empirically motivated data gap distribution of either uniform random or power law form. Missing data segments were patched using segment concatenation, segment filling with average data values, or local interpolation in phase space. We compared results of lamda_1 calculations using complete and patched sets. The greatest proportion of missing data possible that will allow an accurate estimate of lamda_1 depends on the nature of the underlying system and the patching technique used. Self-similar data patched with segment concatenation was particularly robust. Local interpolation in phase space was successful in many cases, but required potentially impractical quantities of intact data as a primer. Optimally, estimates of lamda_1 can readily be recovered with 15% 20% or greater amounts of missing data.

Keywords: largest Lyapunov exponent, simulation, nonlinear analysis, nonlinear dynamics, scaling, missing data