  Comparing paleoclimate time series is complicated by a variety of typical
features, including irregular sampling, age model uncertainty (e.g., errors due
to interpolation between radiocarbon sampling points) and time uncertainty
(uncertainty in calibration), which, taken together, result in unequal and
uncertain observation times of the individual time series to be correlated.
Several methods have been proposed to approximate the joint probability
distribution needed to estimate correlations, most of which rely either on
interpolation or temporal downsampling.
  Here, we compare the performance of some popular approximation methods using
synthetic data resembling common properties of real world marine sediment
records. Correlations are determined by estimating the parameters of a
bivariate Gaussian model from the data using Markov Chain Monte Carlo sampling.
We complement our pseudoproxy experiments by applying the same methodology to a
pair of marine benthic oxygen records from the Atlantic Ocean.
  We find that methods based upon interpolation yield better results in terms
of precision and accuracy than those which reduce the number of observations.
In all cases, the specific characteristics of the studied time series are,
however, more important than the choice of a particular interpolation method.
Relevant features include the number of observations, the persistence of each
record, and the imposed coupling strength between the paired series. In most of
our pseudoproxy experiments, uncertainty in observation times introduces less
additional uncertainty than unequal sampling and errors in observation times
do. Thus, it can be reasonable to rely on published time scales as long as
calibration uncertainties are not known.
