Reconstructing real-world system dynamics from time series data on a single variable is challenging because real-world data often exhibit a highly volatile and irregular appearance potentially driven by several diverse factors. NLTS methods help eliminate less likely drivers of dynamic irregularity. We set a benchmark for regular behavior by investigating how linear systems of ODEs are restricted to exponential and periodic dynamics, and illustrating how irregular behavior can arise if regular linear dynamics are corrupted with noise or shift over time (ie, nonstationarity). We investigate how data can be pre-processed to control for the noise and nonstationarity potentially camouflaging nonlinear deterministic drivers of observed complexity. We can apply signal-detection methods, such as Singular Spectrum Analysis (SSA), to separate signal from noise in the data, and test the signal for nonstationarity potentially …