Abstract
This paper introduces a new class of Bayesian dynamic models for inference and forecasting in high-dimensional time series observed on networks. The new model, called the dynamic chain graph model, is suitable for multivariate time series which exhibit symmetries within subsets of series and a causal drive mechanism between these subsets. The model can accommodate high-dimensional, non-linear and non-normal time series and enables local and parallel computation by decomposing the multivariate problem into separate, simpler sub-problems of lower dimensions. The advantages of the new model are illustrated by forecasting traffic network flows and also modelling gene expression data from transcriptional networks.
Highlights
Multivariate time series are often observed on a network or graph
This paper proposes a new class of multivariate Bayesian dynamic models (West and Harrison, 1997) for time series networks, called dynamic chain graph models
This paper presents a Bayesian dynamic model based on a chain graph which does not rely on the stringent assumptions required for the dynamic graphical model developed in Queen and Smith (1992)
Summary
Multivariate time series are often observed on a network or graph. Despite the everincreasing research on network modelling, statistical dynamic modelling on networks has not been explored much so far (Kolaczyk, 2009, Chapter 9). The multiregression dynamic model (MDM) (Queen and Smith, 1993) is an alternative model that does not require all the component univariate time series to have a common structure This model assumes a conditional independence and causal structure among time series components at each time step, as expressed by a directed acyclic graph (Lauritzen, 1996). This paper presents a Bayesian dynamic model based on a chain graph which does not rely on the stringent assumptions required for the dynamic graphical model developed in Queen and Smith (1992) This new model enables sparsity on chain components, but it allows for unrestricted directed edges between them, accommodating more complex dependence patterns among multivariate time series components. Both applications are examples where the MDM cannot capture all types of dependencies among the time series components
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