Bayesian Analysis of Nonlinear Autoregression Models Based on Neural Networks

In this paper, we show how Bayesian neural networks can be used for time series analysis. We consider a block based model building strategy to model linear and nonlinear features within the time series. A proposed model is a linear combination of a linear autoregression term and a feedforward neural network (FFNN) with an unknown number of hidden nodes. To allow for simpler models, we also consider these terms separately as competing models to select from. Model identifiability problems arise when FFNN sigmoidal activation functions exhibit almost linear behaviour, or when there are almost duplicate or irrelevant neural network nodes. New reversible jump moves are proposed to facilitate model selection mitigating model identifiability problems. We illustrate this methodology analyzing two time series data examples.