A parametric approach to bispectrum estimation

Higher order spectra provide information about processes not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality. The bispectrum which is a third order spectrum provides information about quadratic phase coupling among harmonic components. Bispectrum estimation has been applied in diverse fields principally to obtain such information. Existing methods for bispectrum estimation are patterned after the conventional methods for power spectrum estimation which are known to possess certain limitations. The paper proposes a parametric approach to bispectrum estimation based on AR modeling of time series. The definition and properties of a parametric bispectrum estimator in the general ARMA case are stated. The third moment recursion equations that follow from the model assumptions for the proposed AR bispectrum estimator are presented. The estimates are derived using biased estimates of the third moments in these equations. Results from preliminary experiments suggest that the resulting method does possess certain attractive features when compared with existing methods.