A comparison of spectral estimation methods for the analysis of chaotic and stochastic dynamical systems
Date:
Abstract
Estimating power spectra is frequently a first step in the analysis of stationary time series generated by chaotic and/or stochastic dynamical systems. Accurate estimates are needed for, e.g., data driven modeling and model reduction. Common challenges include the presence of multiple timescales and slow decay of correlations, and when the range of the power spectrum is large. Here, we present a comparison of some spectral estimation methods in current use. We also propose and test a general variance reduction technique, based on the method of control variates, which can be combined with any estimator. We compare these tools on spectral estimation and some related tasks, including spectral factorization and whitening. We apply the techniques to the Kuramoto-Sivashinsky equation, a prototypical model of spatiotemporal chaos.