Periodically integrated subset autoregressions for dutch industrial production and money stock


  • Philip Hans Franses

    1. Econometric Institute, Erasmus University Rotterdam, PO Box 1738, NL-3000 DR Rotterdam, The Netherlands
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    • Is a research fellow of the Royal Netherlands Acadamy of Arts and Sciences, and he is affiliated to the Econometric Institute of the Erasmus University Rotterdam. He obtained an MSc degree in Economics from the University of Groningen and a PhD in Econometrics from the Erasmus University Rotterdam. His main research interests include time series, Seasonality, and model selection. On these topics he has published in several journals, including Economics Letters, Econometric Reviews, Journal of Marketing Research, International Journal of Forecasting, and Oxford Bulletin of Economics and Statistics.


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.