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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 (σARMA) model. This modification allows us to use the EM algorithm to learn parameters and to forecast, even in situations where some data is missing. This modification, in conjunction with the graphical-model approach, also allows us to include cross predictors in situations where there are multiple time series and/or additional non-temporal 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.

ARMA time-series modeling with graphical models