Forecasting using a periodic transfer function: with an application to the UK price of ferrous scrap

The familiar concept of cointegration enables us to determine whether or not there is a long-run relationship between two integrated time series. However, this may not capture short-run effects such as seasonality. Two series which display different seasonal effects can still be cointegrated. Seasonality may arise independently of the long-run relationship between two time series or, indeed, the long-run relationship may itself be seasonal. The market for recycled ferrous scrap displays these features: the US and UK scrap prices are cointegrated, yet the local markets exhibit different forms of seasonality. The paper addresses the problem of using both cointegrating and seasonal relationships in forecasting time series through the use of periodic transfer function models. We consider the problems of testing for cointegration between series with differing seasonal patterns and develop a periodic transfer function model for the US and UK scrap markets. Forecast comparisons with other time series models suggest that forecasting efficiency may be improved by allowing for periodicity but that such improvement is by no means guaranteed. The correct specification of the periodic component of the model is critical for forecast accuracy.