Testing periodically integrated autoregressive models

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.