  This study delves into the domain of dynamical systems, specifically the
forecasting of dynamical time series defined through an evolution function.
Traditional approaches in this area predict the future behavior of dynamical
systems by inferring the evolution function. However, these methods may
confront obstacles due to the presence of missing variables, which are usually
attributed to challenges in measurement and a partial understanding of the
system of interest. To overcome this obstacle, we introduce the autoregressive
with slack time series (ARS) model, that simultaneously estimates the evolution
function and imputes missing variables as a slack time series. Assuming
time-invariance and linearity in the (underlying) entire dynamical time series,
our experiments demonstrate the ARS model's capability to forecast future time
series. From a theoretical perspective, we prove that a 2-dimensional
time-invariant and linear system can be reconstructed by utilizing observations
from a single, partially observed dimension of the system.
