Identifying Chaotic and Quasiperiodic Time-Series Candidates for Efficient Nonlinear Projective Noise Reduction

One of the principal problems in identifying chaos using nonlinear time-series analysis of real-world data is additive noise. A straightforward procedure in traditional phase-space is introduced that can be used to identify data sets amenable to nonlinear projective noise reduction. This methodology can be used both as a tool for identifying candidates for noise reduction and, with some adaptation, for zeroth order noise quantification. Results for simulation data are compared with that for a quasiperiodic measured time series to illustrate when series can benefit most from nonlinear projective noise reduction.