  We study the emergence of pattern formation and chaotic dynamics in the
one-dimensional (1D) generalized Kuramoto-Sivashinsky (gKS) equation by means
of a time-series analysis, in particular a nonlinear forecasting method which
is based on concepts from chaos theory and appropriate statistical methods. We
analyze two types of temporal signals, a local one and a global one, finding in
both cases that the dynamical state of the gKS solution undergoes a transition
from high-dimensional chaos to periodic pulsed oscillations through
low-dimensional deterministic chaos with increasing the control parameter of
the system. Our results demonstrate that the proposed nonlinear forecasting
methodology allows to elucidate the dynamics of the system in terms of its
predictability properties.
