TESTING PERIODICALLY INTEGRATED AUTOREGRESSIVE MODELS

Periodically integrated time series require a periodic differencing fi lter to remove the stochastic trend. A non-periodic integrated time se ries needs the first-difference filter for similar reasons. When the c hanging seasonal fluctuations for the nonperiodic integrated series ca n 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] a re used to distinguish between these two alternative stochastic and no n-stochastic seasonal processes when there is a single known structura l break in the seasonal dummy parameters. Two empirical examples, name ly, the logarithms of quarterly real GNP series for Austria and German y, are used to illustrate the approach.