Asymptotic properties of higher-order periodograms

Correlation properties of periodograms of third order and of the cumulant periodogram of fourth order are studied. The periodograms are used by the author to construct nonparametric estimators of the bispectral and trispectral density, respectively, of a strictly stationary stochastic process with discrete time. We also indicate conditions under which each of the above-mentioned periodograms is an asymptotically unbiased estimator of the corresponding spectral density.