Cumulant-based autocorrelation estimates of non-Gaussian linear processes

Autocorrelation of linear random processes can be expressed in terms of their cumulants. Theoretical insensitivity of the latter to additive Gaussian noise of unknown covariance, is exploited in this paper to develop (within a scale) autocorrelation estimators of linear non-Gaussian time series using cumulants of order higher than two. Windowed projections of third-order cumulants are shown to yield strongly consistent estimators of the autocorrelation sequence. Both batch and recursive algorithms are derived. Asymptotic variance expressions of the proposed estimators are also presented. Simulations are provided to illustrate the performance of the proposed algorithms and compare them with conventional approaches.