  We present the general relationship between phase correlations and the
hierarchy of polyspectra in the Fourier space, and the new theoretical
understanding of the phase information is provided. Phase correlations are
related to the polyspectra only through the non-uniform distributions of the
phase sum $\theta_{\sbfm{k}_1} + ... + \theta_{\sbfm{k}_N}$ with closed wave
vectors, $\bfm{k}_1 + ... + \bfm{k}_N = 0$. The exact relationship is given by
the infinite series, which one can truncate in a consistent manner. The method
to calculate the series to arbitrary order is explained, and the explicit
expression of the first-order approximation is given. A numerical demonstration
proves that the distribution of the phase sum is a robust estimator and
provides an alternative statistic to search for the non-Gaussianity.
