  In this paper, we predict the covariance matrices of both the power spectrum
and the bispectrum, including full non-Gaussian contributions, redshift space
distortions, linear bias effects and shot-noise corrections, using perturbation
theory (PT). To quantify the redshift-space distortion effect, we focus mainly
on the monopole and quadrupole components of both the power and bispectra. We,
for the first time, compute the 5- and 6-point spectra to predict the
cross-covariance between the power and bispectra, and the auto-covariance of
the bispectrum in redshift space. We test the validity of our calculations by
comparing them with the covariance matrices measured from the MultiDark-Patchy
mock catalogues that are designed to reproduce the galaxy clustering measured
from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that
the simple, leading-order perturbation theory works because the shot-noise
corrections for the Patchy mocks are more dominant than other higher-order
terms we ignore. In the meantime, we confirm some discrepancies in the
comparison, especially of the cross-covariance. We discuss potential sources of
such discrepancies. We also show that our PT model reproduces well the
cumulative signal-to-noise of the power spectrum and the bispectrum as a
function of maximum wavenumber, implying that our PT model captures
successfully essential contributions to the covariance matrices.
