AR‐modelling bispectrum estimation – A comparison of existing methods and new contributions

This paper deals with bispectrum estimation via autoregressive (AR) modelling of a process contaminated by additive Gaussian noise (white and coloured). Two main contributions are provided in this work. First, a comparison between the existing third order recursion (TOR) and the constrained third order mean (CTOM) methods is presented. Basically, the second method is shown to be a smoothing windowed version (i.e. a covariance‐type estimator) of the first one, achieved at the expense of the loss of the recursivity in the AR‐model order. This prior analysis has induced us to develop an alternative scheme to tackle this type of problem, which, while maintaining the main feature of the CTOM method as a covariance type estimator, is a recursive‐in‐order algorithm. This recursivity is obtained carrying out an appropriate minimization procedure of some prediction squared errors also defined here. The paper also compares, by means of simulations, this proposed method and the two existing ones.