A Bayesian analysis of periodic integration

Abstract

Recent empirical research into the seasonal and trend properties of macroeconomic time series using periodic models has resulted in strong evidence in favour of periodic integration (PI). PI implies that the dierencing ®lter necessary to remove a stochastic trend varies across seasons and, hence, that seasonal¯uctuations are related to the stochastic trend. Previous studies ®nding 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 macroeconomic 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.