Abstract

We present a prototype that we have developed for analyzing so-called stochastic ARMA models in SQL Server 2005, Analysis Services. The class of stochastic ARMA models extends the classic ARMA time-series models by replacing (or smoothing) the deterministic relationship between target and regressors in these models with a conditional Gaussian distribution having a small controllable variance. As this variance approaches zero, a stochastic ARMA model approaches a classic ARMA model. We represent a stochastic ARMA model as a directed graphical model. In doing so, we benefit from the ability to apply standard graphical-model-inference algorithms during parameter estimation (including estimation in the presence of time series with incomplete data), model selection, and prediction. The graphical model representation also offers a visual representation that is easy to interpretate. We demonstrate how the graphical representation in this way lends itself as a conceptually easy way of extending the models to handling cross predicting time series, periodicity, and trends.

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