Writing in this journal, Sumner (2004) advocates use of long lag lengths when conducting co-integration tests. Replication of Sumner's consumption model suggests long lag lengths are a mis-specification: the true underlying model is periodic. We test for periodically distributed unit roots - unit roots that differ with the season and vary with past behaviour. Co-integration between income and consumption, based on a periodic error correction model, is rejected. A PADL specification is preferred for modelling the income-consumption relationship, using seasonally unadjusted data.