New modifications of second- and third-order periodograms

New modifications of the second- and third-order periodograms are described which serve as “half-finished products” in constructing statistical estimators for the spectral and bispectral densities, respectively, of a strictly stationary stochastic process $\{X(k), k\in \mathbb Z\}$. A distinguishing feature of both modified periodograms is essentially the smaller value of their variances in comparison to those for previously know modifications.