Testing for Integration using Evolving Trend and Seasonals Models: A Bayesian Approach

In this paper, we make use of state space models toinvestigate the presence of stochastic trends in economic time series. Amodel is specified where such a trend can enter either in the autoregressiverepresentation or in a separate state equation. Tests based on the formerare analogous to Dickey-Fuller tests of unit roots, while the latter areanalogous to KPSS tests of trend-stationarity. We use Bayesian methods tosurvey the properties of the likelihood function in such models and tocalculate posterior odds ratios comparing models with and without stochastictrends. We extend these ideas to the problem of testing for integration atseasonal frequencies and show how our techniques can be used to carry outBayesian variants of either the HEGY or Canova-Hansen test. Stochasticintegration rules, based on Markov Chain Monte Carlo, as well asdeterministic integration rules are used. Strengths and weaknesses of eachapproach are indicated.