  We propose a Bayesian nonparametric model based on Markov Chain Monte Carlo
(MCMC) methods for the joint reconstruction and prediction of discrete time
stochastic dynamical systems, based on $m$-multiple time-series data, perturbed
by additive dynamical noise. We introduce the Pairwise Dependent Geometric
Stick-Breaking Reconstruction (PD-GSBR) model, which relies on the construction
of a $m$-variate nonparametric prior over the space of densities supported over
$\mathbb{R}^m$. We are focusing in the case where at least one of the
time-series has a sufficiently large sample size representation for an
independent and accurate Geometric Stick-Breaking estimation, as defined in
Merkatas et al. (2017). Our contention, is that whenever the dynamical error
processes perturbing the underlying dynamical systems share common
characteristics, underrepresented data sets can benefit in terms of model
estimation accuracy. The PD-GSBR estimation and prediction procedure is
demonstrated specifically in the case of maps with polynomial nonlinearities of
an arbitrary degree. Simulations based on synthetic time-series are presented.
