A Bayesian analysis of smooth transitions in trend

Many real time series exhibit changes in trend. However, because the observed changes are frequently not abrupt, models that specify step changes do not adequately represent the observed behavior. Smooth transition models allow for a smooth change from one linear regime to the next. This paper is concerned with parameter estimation and prediction for a linear trend model with a smooth transition in both the intercept and slope. The smooth transition is modelled using a logistic transition function. We present a Bayesian approach to inference for this model that allows for an autocorrelated error structure and uses the exact likelihood. We develop a slice sampler for the analysis. We apply the analysis to a published macroeconomic data set which exhibits a slowly changing time trend.