  The long-term variations in the orbit of the Earth govern the insolation on
its surface and hence its climate. The use of the astronomical signal, whose
imprint has been recovered in the geological records, has revolutionized the
determination of the geological timescales. However, the orbital variations
beyond 60 Myr cannot be reliably predicted because of the chaotic dynamics of
the planetary orbits in the Solar System. Taking this dynamical uncertainty
into account is necessary for a complete astronomical calibration of geological
records. Our work addresses this problem with a statistical analysis of 120 000
orbital solutions of the secular model of the Solar System ranging from 500 Myr
to 5 Gyr. We obtain the marginal probability density functions of the
fundamental secular frequencies using kernel density estimation. The
uncertainty of the density estimation is also obtained here in the form of
confidence intervals determined by the moving block bootstrap method. The
results of the secular model are shown to be in good agreement with those of
the direct integrations of a comprehensive model of the Solar System.
Application of our work is illustrated on two geological data sets: the
Newark-Hartford records and the Libsack core.
