Periodically integrated subset autoregressions for Dutch industrial production and money stock

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.