An iterative non-parametric approach to the estimation of polyspectra

A number of powerful tools for analyzing linear and nonlinear data sets are based on various spectral measures. In particular, the bispectrum is commonly used for testing Gaussianity and linearity. Due to their inherent robustness to model assumptions, non-parametric estimators of the polyspectra are of particular importance. Unfortunately, the most commonly used non-parametric estimator, the windowed-periodogram, suffers from large sidelobes and fails to provide high-resolution estimates. In this paper, we develop a non-parametric estimator that utilizes the recently introduced iterative adaptive approach (IAA) to provide high-resolution estimates of the polyspectra for nonlinear data. Using the IAA method, we first obtain estimates of the spectral amplitudes and the covariance matrix iteratively, and then use the spectral amplitudes to form accurate estimates of the polyspectra. The developed estimator can be extended to the application of unevenly sampled data, and can also be used in the statistically efficient estimation of coherence polyspectra. The effectiveness of the proposed estimator is demonstrated with both real and simulated data.