ARMA Time-Series Modeling with Graphical Models

TL;DR

This paper reformulates ARMA models as graphical models, introduces a stochastic variant to enable EM-based learning and forecasting with missing data, and demonstrates improved accuracy and flexibility in multivariate and covariate-rich scenarios.

Contribution

The paper presents a novel stochastic ARMA model using Gaussian noise, enabling EM algorithm application and enhanced modeling capabilities over traditional deterministic ARMA.

Findings

EM algorithm enables parameter learning with missing data

Stochastic ARMA improves smoothing and forecasting accuracy

Inclusion of cross predictors enhances model performance

Abstract

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.