Periodically integrated time series require a periodic differencing filter to remove the stochastic trend. A non-periodic integrated time series needs the first-difference filter for similar reasons. When the changing seasonal fluctuations for the non-periodic integrated series can be described by seasonal dummy variables for which the corresponding parameters are not constant within the sample, such a series may not be easily distinguished from a periodically integrated time series. In this paper, testing procedures developed by Franses and McAleer [4] are used to distinguish between these two alternative stochastic and non-stochastic seasonal processes when there is a single known structural break in the seasonal dummy parameters. Two empirical examples, namely, the logarithms of quarterly real GNP series for Austria and Germany, are used to illustrate the approach.

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Keywords autoregressive models, time series
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Journal Mathematics and Computers in Simulation
Franses, Ph.H.B.F, & McAleer, M.J. (1997). Testing periodically integrated autoregressive models. Mathematics and Computers in Simulation, 457–465. doi:10.1016/S0378-4754(97)00032-3