Bispectrum estimation using a MISO autoregressive model

Abstract

Bispectra are third-order statistics that have been used extensively in analyzing nonlinear and non-Gaussian data. Bispectrum of a process can be computed as the Fourier transform of its bicumulant sequence. It is in general hard to obtain reliable bicumulant samples at high lags since they suffer from large estimation variance. This paper proposes a novel approach for estimating bispectrum from a small set of given low lag bicumulant samples. The proposed approach employs an underlying MISO system composed of stable and causal autoregressive components. We provide an algorithm to compute the parameters of such a system from the given bicumulant samples. Experimental results show that our approach is capable of representing non-polynomial spectra with a stable underlying system model, which results in better bispectrum estimation than the leading algorithm in the literature.