Traditional methods for the analysis of seasonal and nonstationary time series assume that seasonality and a stochastic trend can be separated in some way. However, several macroeconomic time series display patterns which indicate that separation may not be valid. Such patterns occur if seasonal movements change slowly over time and the timing of changes depends on exogenous shocks from e.g., a business cycle. Periodic autoregressive processes with unit roots are suitable for modeling and forecasting such series. Using Monte-Carlo simulations the Census X-11 adjustment and the Box-Jenkins analysis are compared considering the case that the data are generated by periodic processes. It appears, for example, that the intrinsic periodicity is removed only partially, that a test for a unit root is robust, and that the most sensible practical strategy seems to be to start with a general periodic autoregressive model. If necessary, one can then switch to a usual seasonal adjustment procedure if the hypothesis of nonperiodicity cannot be rejected. The quartely real German GNP series is used to illustrate that a periodic model can yield superior modeling and forecasting.

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Computational Statistics & Data Analysis
Erasmus School of Economics

Franses, P. H. (1995). The effects of seasonally adjusting a periodic autoregressive process. Computational Statistics & Data Analysis, 683–704. doi:10.1016/0167-9473(94)00019-F