The univariate quarterly Dutch series of industrial production and money stock are both modelled with a periodically integrated subset autoregression (PISA). This model for a non-stationary series allows the lag orders, the values of the parameters and the cyclical patterns to vary over the seasons. The PISA models are found by applying a general-to-simple specification strategy, which deals with non-stationarity and periodicity simultaneously. It is found that the two series show a common asymmetric cyclical behaviour. This paper further proposes a test for periodicity in the errors, with which it is argued that a non-periodic model for the industrial production and money stock is misspecified and that seasonal adjustment does not remove periodicity in the autocorrelation function.

Dutch industry, non-stationary seasonal time series, periodicity, seasonal adjustment,
Journal of Forecasting
Erasmus School of Economics

Franses, Ph.H.B.F. (1993). Periodically integrated subset autoregressions for Dutch industrial production and money stock. Journal of Forecasting, 601–613. doi:10.1002/for.3980120706