Abstract
Assume X-1, X-2,.., X-N are realizations of N observations from a real-valued discrete parameter third-order stationary process X(t,)t = 0 +/- 1,+/- 2,..., with bispectrum f(XXX)(lambda(1), lambda(2)) where "-pi <= lambda(1), lambda(2 )<= pi". Based on the previous assumption, L different multitapered biperiodograms I-XXX((mt)j)(lambda(1), lambda(2)); j = 1, 2,..., L on overlapped segments (X-t((j));1 <= t < N) can be constructed. Further, the mean and variance of the average of these different multitapered biperiodograms can be expressed as asymptotic expressions. According to different bispectral windows/kernels (W-beta((j))(alpha(1),alpha(2)), where "-pi <= alpha(1), alpha(2) <= pi" and beta is the bandwidth) and I-XXX((mt)j)(lambda(1), lambda(2)), the bispectrum f(XXX)(lambda(1), lambda(2)) can be estimated. The asymptotic expressions of the first- and second-ordered moments as well as the integrated relative mean squared error (IMSE) of this estimate are derived. Finally, some estimation results based on numerically generated data from the selected process "DCGINAR(1)" are presented and discussed in detail.