Periodic integration: further results on model selection and forecasting

This paper considers model selection and forecasting issues in two closely related models for nonstationary periodic autoregressive time series PAR]. Periodically integrated seasonal time series PIAR] need a periodic differencing filter to remove the stochastic trend. On the other hand, when the nonperiodic first order differencing filter can be applied, one can have a periodic model with a nonseasonal unit root PARI]. In this paper, we discuss and evaluate two testing strategies to select between these two models. Furthermore, we compare the relative forecasting performance of each model using Monte Carlo simulations and some U.K. macroeconomic seasonal time series. One result is that forecasting with PARI models while the data generating process is a PIAR process seems to be worse thanvice versa.