A new class of space-time models derived from standard dynamic factor models is proposed. The temporal dependence is modeled by latent factors while the spatial dependence is modeled by the factor loadings. Factor analytic arguments are used to help identify temporal components that summarize most of the spatial variation of a given region. The temporal evolution of the factors is described in a number of forms to account for different aspects of time variation such as trend and seasonality. The spatial dependence is incorporated into the factor loadings by a combination of deterministic and stochastic elements thus giving them more flexibility and generalizing previous approaches. The new structure implies nonseparable space-time variation to observables, despite its conditionally independent nature, while reducing the overall dimensionality, and hence complexity, of the problem. The number of factors is treated as another unknown parameter and fully Bayesian inference is performed via a reversible jump Markov Chain Monte Carlo algorithm. The new class of models is tested against one synthetic dataset and applied to pollution data obtained from the Clean Air Status and Trends Network (CASTNet). Our factor model exhibited better predictive performance when compared to benchmark models, while capturing important aspects of spatial and temporal behavior of the data.
In this paper, we propose a fully Bayesian approach to the special class of nonlinear time-series models called the logistic smooth transition autoregressive (LSTAR) model. Initially, a Gibbs sampler is proposed for the LSTAR where the lag length, k, is kept fixed. Then, uncertainty about k is taken into account and a novel reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is proposed. We compared our RJMCMC algorithm with well-known information criteria, such as the Akaike's information criteria, the Bayesian information criteria (BIC) and the deviance information criteria. Our methodology is extensively studied against simulated and real-time series. Copyright 2005 Blackwell Publishing Ltd.
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