Hierarchical Dynamic Beta Model

Abstract

We develop a hierarchical dynamic Bayesian beta model for modelling a set of time series of rates or proportions. The proposed methodology enables to combine the information contained in different time series so that we can describe a common underlying system, which is though flexible enough to allow the incorporation of random deviations, related to the individual series, not only through time but also across series. That allows to fit the case in which the observed series may present some degree of level shift. Additionally, the proposed model is adaptive in the sense that it incorporates precision parameters that can be heterogeneous no only over time but also across the series. Our methodology was applied to both real and simulated data. The real data sets used in this article include three time series of Brazilian monthly unemployment rates, observed in the cities of Recife, S˜ao Paulo and Porto Alegre, in the period from March 2002 to March 2012. A new parametrization of the precision parameter makes possible the use of the same type of link function for both the mean and the precision parameters, which are then expressed in the (0, 1) interval, providing a more meaningful interpretation in terms of the magnitude of the scale.