Bicorrelation & bispectrum non parametric & parametric approaches

A new class of non-Gaussian processes is introduced. They are obtained by squaring Gaussian ARMA processes and are thus called QARMA processes. Theoretical properties of QARMA processes are derived in terms of their bicorrelation, bispectrum and bi-z-density. They happen to exhibit pertinent parameters on particular axes named hereafter principal axes. A lower bound of the variance of the bicorrelation estimate is derived based on a novel approach that makes use of Hermite polynomials. Its value is confirmed by simulation. Calibration abacusses giving the number of samples required by a specific accuracy are drawn. The effects of measurement samples, observation samples, smoothing and sample rate are taken into account. The robustness with respect to an additive (quantization included) or multiplicative noise is studied. The bicorrelogram obtained by the Fourier transform of the windowed bicorrelation is processed. Robustness and performance are studied.