Characterising Economic Trends by Bayesian Stochastic Model Specification Search

A recently proposed Bayesian model selection technique, stochastic model specification search, is carried out to discriminate between two trend generation hypotheses. The first is the trend-stationary hypothesis, for which the trend is a deterministic function of time and the short run dynamics are represented by a stationary autoregressive process. The second is the difference-stationary hypothesis, according to which the trend results from the cumulation of the effects of random disturbances. A difference-stationary process may originate in two ways: from an unobserved components process adding up an integrated trend and an orthogonal transitory component, or implicitly from an autoregressive process with roots on the unit circle. The different trend generation hypotheses are nested within an encompassing linear state space model. After a reparameterisation in non-centred form, the empirical evidence supporting a particular hypothesis is obtained by performing variable selection on the model components, using a suitably designed Gibbs sampling scheme. The methodology is illustrated with reference to a set of US macroeconomic time series which includes the traditional Nelson and Plosser dataset. The conclusion is that most series are better represented by autoregressive models with time-invariant intercept and slope and coefficients that are close to boundary of the stationarity region. The posterior distribution of the autoregressive parameters provides useful insight on quasi-integrated nature of the specifications selected.