Hierarchical Bayesian Modelling for Spatial Time Series: An Alternative Approach to Spatial SUR

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Despite the fact that the amount of datasets containing long economic time series with a spatial reference has significantly increased during the years, the presence of integrated techniques that aim to describe the temporal evolution of the series while accounting for the location of the measurements and their neighboring relations is very sparse in the econometric literature. This paper shows how the Hierarchical Bayesian Space Time model presented by Wikle, Berliner and Cressie (Environmental and Ecological Statistics, l998) for temperature modeling, can be tailored to model relationships between variables that have both a spatial and a temporal reference. The first stage of the hierarchical model includes a set of regression equations (each one corresponding to a different location) coupled with a dynamic space-time process that accounts for the unexplained variation. At the second stage, the regression parameters are endowed with priors that reflect the neighboring relations of the locations under study; moreover, the spatio-temporal dependencies in the dynamic process for the unexplained variation are being established. Putting hyperpriors on previous stages’ parameters completes the Bayesian formulation, which can be implemented in a Markov Chain Monte Carlo framework. The proposed modeling strategy is useful in quantifying the temporal evolution in relations between economic variables and this quantification may serve for excess forecasting accuracy.

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