A Bayesian approach to model selection in stochastic coefficient regression models and structural time series models

A Bayesian model selection procedure is proposed for a stochastic coefficient regression model to determine which coefficients are fixed and which are time-varying. The posterior probabilities are computed by Gaussian quadrature using the Kalman filter. It is shown empirically that the model selection approach works well on both simulated and real data. A similar approach can be used to select a model from a class of state space models. In particular, for a trend plus seasonal structural time series model we show how to determine if the trend and/or seasonal component is deterministic or stochastic.