Forecasting with periodic models: A comparison with time invariant coefficient models

Working with seventeen quarterly UK macroeconomic variables, characterized as periodically integrated in Franses and Romijn, we have found that unconstrained periodic models do not beat time invariant alternatives in forecasting, even when cointegrating relationships among the seasons are taken into account. However, when appropriately constrained, the forecasting performance of periodic models can be much better than that of non-periodic models. Homogeneity restrictions among some seasons seem to be very important in that respect, which motivates us to propose switching for specific quarters between a periodic model and a non-periodic univariate auto-regression to better capture the behaviour of these variables. Once season homogeneity is taken into account, incorporating the cointegrating relationships among the seasons through periodic error correction models achieves a substantial additional forecasting improvement.