  This work addresses the problem of missing data in time-series analysis
focusing on (a) estimation of model parameters in the presence of missing data
and (b) reconstruction of missing data. Standard approaches used to solve these
problems like the maximum likelihood estimation or the Bayesian inference rely
on a priori assumptions like the Gaussian or stationary behavior of missing
data and might lead to biased results where these assumptions are unfulfilled.
In order to go beyond, we extend the Finite Element Methodology (FEM) for
Vector Auto-Regressive models with eXogenous factors and bounded variation of
the model parameters (FEM-VARX) towards handling the missing data problem. The
presented approach estimates the model parameters and reconstructs the missing
data in the considered time series and in the involved exogenous factors,
simultaneously. The resulting computational framework was compared to the
state-of-art methodologies on a set of test-cases and is available as
open-source software.
