  We express the classic ARMA time-series model as a directed graphical model.
In doing so, we find that the deterministic relationships in the model make it
effectively impossible to use the EM algorithm for learning model parameters.
To remedy this problem, we replace the deterministic relationships with
Gaussian distributions having a small variance, yielding the stochastic ARMA
(ARMA) model. This modification allows us to use the EM algorithm to learn
parmeters and to forecast,even in situations where some data is missing. This
modification, in conjunction with the graphicalmodel approach, also allows us
to include cross predictors in situations where there are multiple times series
and/or additional nontemporal covariates. More surprising,experiments suggest
that the move to stochastic ARMA yields improved accuracy through better
smoothing. We demonstrate improvements afforded by cross prediction and better
smoothing on real data.
