Trispectral analysis of stationary stochastic processes: Large-sample case (Q1177489)

Let \(\{\xi(k)\}\) be a discrete stationary process possessing a trispectral density \(f^{(4)}(\lambda)\) where \(\lambda=(\lambda_ 1,\lambda_ 2,\lambda_ 3)\). It is assumed that two independent realizations of length \(2n+1\) are given. One of them is divided into several non-overlapping (or partially overlapping) parts. Using the Parzen window, from each part the integrated periodogram of fourth order is calculated. Then the periodograms are averaged and thus an estimator \(I_ n(\lambda)\) for \(f^{(4)}(\lambda)\) is obtained. The author proves that \[ \sup| E I_ n(\lambda)-f^{(4)}(\lambda)|=O(n^{-2}). \]