  {We consider the problem of estimating causal influences between observed
processes from time series possibly corrupted by errors in the time variable
(dating errors) which are typical in palaeoclimatology, planetary science and
astrophysics. "Causality ratio" based on the Wiener -- Granger causality is
proposed and studied for a paradigmatic class of model systems to reveal
conditions under which it correctly indicates directionality of unidirectional
coupling. It is argued that in case of {\it a priori} known directionality, the
causality ratio allows a characterization of dating errors and observational
noise. Finally, we apply the developed approach to palaeoclimatic data and
quantify the influence of solar activity on tropical Atlantic climate dynamics
over the last two millennia. A stronger solar influence in the first millennium
A.D. is inferred. The results also suggest a dating error of about 20 years in
the solar proxy time series over the same period.
