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.

本研究将经典 ARMA 时间序列模型表达成有向图形式，在此基础上将确定性关系替换为小方差的高斯分布，形成随机 ARMA（ARMA）模型，这种改进允许我们使用 EM 算法学习参数并进行预测，即使存在数据丢失。实验结果表明，移动到随机 ARMA 模型能够通过更好的平滑获得更高的精度，并演示了交叉预测和更好平滑的改进在实际数据上的效果。