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

The familiar concept of cointegration enables us to determine whether or no t there is a long-run relationship between two integrated time series. Howe ver, this may not capture short-run effects such as seasonality. Two series which display different seasonal effects can still be cointegrated. Season ality may arise independently of the long-run relationship between two time series or, indeed, the long-run relationship may itself be seasonal. The m arket for recycled ferrous scrap displays these features: the US and UK scr ap prices are cointegrated, yet the local markets exhibit different forms o f seasonality. The paper addresses the problem of using both cointegrating and seasonal relationships in forecasting time series through the use of pe riodic transfer function models, We consider the problems of testing for co integration between series with differing seasonal patterns and develop a p eriodic transfer function model for the US and UK scrap markets. Forecast c omparisons with other time series models suggest that forecasting efficienc y 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. (C) 1999 Elsevier Science B.V. All rights reserved.