A Semiadaptive Smoothing Algorithm in Bispectrum Estimation

Fourier transform is used to calculate the third-order periodogram, which is an unbiased estimation of the bispectrum. However, the Fourier transform has energy leakage at adjacent frequencies, and the third-order periodogram is not a consistent estimator of the bispectrum because the variance does not converge toward zero when the sample size increases. To solve these problems, we used the Kolmogorov-Zurbenko Fourier transform (KZFT) to calculate the third-order periodogram and then adaptively smoothed it using a square window with varying bandwidth. At each paired frequencies, the bandwidth of the square window is expanded until the squared variation within the window reached a prespecified percentage of the total squared variation. The algorithm gave good results on simulated data, separating two close frequency components with very different energies in noisy data.