Abstract.In this paper we consider the estimation of the fourth‐order cumulant spectral density. Indeed this is the first case where the cumulant depends on lower‐order product moments for a mean‐zero stationary process. The proposed estimator of the fourth‐order cumulant spectral density is constructed by replacing product moments with appropriately weighted estimates of product moments according to the definition of the fourth‐order cumulant spectral density. Asymptotic unbiasedness and consistency are shown to hold for these estimators under stationarity and absolute summability of cumulants up to various orders with no restrictions on the frequencies. An expression for the asymptotic variance is also
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