Multiwindow bispectral estimation

The bispectral density provides crucial information about non-Gaussian and/or non-linear properties of stochastic processes. In practice however, bispectral estimators are prone to be inaccurate and statistically inconsistent. In this paper we have discussed the statistical properties of non-parametric direct bispectral estimators. Several multitaper based bispectral estimators are presented, including a recently developed approach giving better frequency resolution. We will show that the bias and variance of these estimators are governed mainly by a quantity we call the total bispectral window. Our conclusion is that classical bispectral estimations, using biperiodograms in combination with tapering and/or bifrequency smoothing, are outperformed by the multitaper based bispectral estimators presented in this paper.