Transfer functions in dynamic generalized linear models

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.