, Volume 37, Issue 1, pp 33-52

Periodic integration: further results on model selection and forecasting

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Abstract

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.

This research was sponsored by the Economic Research Foundation, which is a part of the Netherlands Organization for Scientific Research (N.W.O.). The first author thanks the financial support from the Royal Netherlands Academy of Arts and Sciences. Part of the material in this paper has been presented at seminars at Tulane University and Brown University Several discussions with Eric Ghysels and Hahn Lee proved to be very helpful. Comments from an anonymous referee are gratefully acknowledged.