Trispectral Analysis of Stationary Stochastic Processes: Large-Sample Case

We consider the trispectral density $f^{(4)}(\lambda_1,\lambda_2,\lambda_3)$ of a stationary stochastic process $\{\xi(k),\ k\in\mathbf Z\}$ for the case where the full realization of the stochastic process $\xi(k)$ cannot be processes in its entirety on the available computer. The trispectral density estimator is constructed as the arithmetic mean of the estimators obtained using a finite number of smaller nonoverlapping (or partially overlapping) arrays. A specific technique is proposed which substantially improves the estimation quality of the function $f^{(4)}(\lambda_1,\lambda_2,\lambda_3)$ in this case.