Trends, lead times and forecasting

The innovations representation for a local linear trend can adapt to long run secular and short term transitory effects in the data. This is illustrated by the theoretical power spectrum for the model which may possess considerable power at frequencies that might be associated with cycles of several years' duration. Whilst advantageous for short term forecasting, the model may be of less use when interest is in the underlying long run trend in the data. In this paper we propose a generalisation of the innovations representation for a local linear trend that is appropriate for representing short, medium and long run trends in the data.