Statistical Modelling 10 (2010), 3–40
Transfer functions in dynamic generalized linear models
Mariane B Alves
Instituto de Matemática e Estatística
UERJ
Rua São Francisco Xavier, 524
Pavilhão João Lyra Filho 6° andar
Diretoria - Sala 6019-Bloco B - RJ - Brazil 20559-900
Brazil
eMail: mariane@ime.uerj.br
Dani Gamerman
Departamento de Métodos Estatísticos
Instituto de Matemática
UFRJ
Brazil
Marco AR Ferreira
Department of Statistics
University of Missouri
USA
Abstract:
In a time series analysis it is sometimes necessary to assume that the
effect of a regressor does not have only immediate impact on the mean
response, but that its effects somehow propagate to future times. We
adopt, in this work, transfer functions to model such impacts,
represented by structural blocks present in dynamic generalized linear
models. All the inference is carried under the Bayesian paradigm.
Two sources of difficulties emerge for the analytical derivation of
posterior distributions: non-Gaussian nature of the response,
associated to non-conjugate priors and also non-linearity of the
predictor on auto regressive parameters present in transfer functions.
The purpose of this work is to produce full Bayesian inference on
dynamic generalized linear models with transfer functions, using
Markov chain Monte Carlo methods to build samples of the posterior
joint distribution of the parameters involved in such models. Several
transfer structures are specified, associated to Poisson, Binomial,
Gamma and inverse Gaussian responses. Simulated data are analyzed
under the resulting models in order to assess their performance.
Finally, two applications to real data concerning environmental
sciences are made under different model formulations.
Keywords:
Bayesian inference; dynamic generalized linear models;
Markov chain Monte Carlo; transfer functions
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