  In this paper, we present a new bivariate model for the joint description of
the Bitcoin prices and the media attention to Bitcoin. Our model is based on
the class of the L\'evy processes and is able to realistically reproduce the
jump-type dynamics of the considered time series. We focus on the low-frequency
setup, which is for the L\'evy - based models essentially more difficult than
the high-frequency case. We design a semiparametric estimation procedure for
the statistical inference on the parameters and the L\'evy measures of the
considered processes. We show that the dynamics of the market attention can be
effectively modelled by the L\'evy processes with finite L\'evy measures, and
propose a data-driven procedure for the description of the Bitcoin prices.
