Mining Cross-predicting Stochastic ARMA Time
Series In SQL Server 2005
Author(s)
B. Thiesson & J. Lind
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.
Keywords: time series, graphical models, ARMA, Bayes net, SQL server.
1 Introduction
Graphical models have been used to represent time-series models for almost two
decades (e.g., Dean and Kanazawa [1]; Cooper et al. [2]). The benefits of such
representation include the ability to apply standard graphical-model-inference
algorithms for parameter estimation (including estimation in the presence of
missing data), for model selection, and for prediction. We introduce the most
fundamental concepts for this class of models when needed in this paper. A gentle
introduction and more details can be found in, for instance, Jensen [3].
Keywords
time series, graphical models, ARMA, Bayes net, SQL server.
Related Book
Other papers in this volume
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