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.

autoregressive models, time series,
Mathematics and Computers in Simulation
Erasmus School of Economics

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