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 sea- sonal fluctuations for the non-periodic integrated series can be described by seasonal dummy variables for which the corresponding parameters are not constant within the sampie, such a series may not be easily & stinguished from a periodically integrated time series. In this paper, nested and non-nested testing procedures are proposed to distinguish between these two alternative stochastic and non-stochastic seasonal processes, When it is assumed there is a single unknown structural break in the seasonal dummy parameters. Several empirical examples using quarterly real macroeconomic time series for the United Kingdom illustrate the nested and non-nested approaches.

model selection, periodicity, seasonality,
Communications in Statistics: Theory and Methods
Erasmus School of Economics

Franses, Ph.H.B.F, & McAleer, M.J. (1997). Testing nested and non-nested periodically integrated autoregressive models. Communications in Statistics: Theory and Methods, 1461–1475. doi:10.1080/03610929708831993