Hello and welcome to the community 
What kind of data are you modelling? Would a statespace model on the form
\begin{aligned}
x(k+1) &= Ax(k) + Bu(k) + Ew(k) \\
y(k) &= Cx(k) + w(k)
\end{aligned}
work? This kind of model can be easily converted to an multivariate ARX model after estimation if required.
what kind of analysis are you interested in performing? There are a few model-validation methods implemented in ControlSystemIdentification.jl, but they don’t really target the time-series usecase as much as they do the system-identification use case. See also this post for several packages targeting time-series use cases.