A Bayesian analysis of periodic integration

Recent empirical research into the seasonal and trend properties of macro-economic time series using periodic models has resulted in strong evidence in favour of periodic integration (PI). PI implies that the differencing filter necessary to remove a stochastic trend varies across seasons and, hence, that seasonal fluctuations are related to the stochastic trend. Previous studies finding evidence of PI have used classical econometric techniques. In this paper, we investigate the possible sensitivity of this empirical result by using Bayesian techniques. An application of posterior odds analysis and highest posterior density interval tests to several quarterly UK macro-economic series suggests strong evidence for PI, even when we allow for structural breaks in the deterministic seasonals. A predictive exercise indicates that PI usually outperforms other competing models in terms of out-of-sample forecasting.