  We make the first attempt to estimate and interpret the biphase data for
astronomical time series. The biphase is the phase of the bispectrum, which is
the Fourier domain equivalent of the three-point correlation function. The
bispectrum measures two key nonlinear properties of a time series -- its
reversability in time, and the symmetry about the mean of its flux distribution
-- for triplets of frequencies. Like other Fourier methods, it is especially
valuable for working with time series which contain large numbers of cycles at
the period of interest, but in which the signal-to-noise at a given frequency
is small in any individual cycle, either because of measurement errors, or
because of the contributions from signals at other frequencies. This has long
been the case for studies of X-ray binaries, but is increasingly becoming true
for stellar variability (both intrinsic and due to planetary transits) in the
Kepler era. We attempt in this paper also to present some simple examples to
give a more intuitive understanding of the meaning of the bispectrum to
readers, in order to help to understand where it may be applicable in
astronomy. In particular, we give illustrative examples of what biphases may be
shown by common astrophysical time series such as pulsars, eclipsers, stars in
the instability strip, and solar flares. We then discuss applications to the
biphase data for understanding the shapes of the quasi-periodic oscillations of
GRS 1915+105 and the coupling of the quasi-periodic oscillations to the
power-law noise in that system.
