Trends, Lead Times and Forecasting

The local linear trend and global linear trend models embody extreme assumptions about trends. According to the local linear trend formulation the level and growth rate are allowed to rapidly adapt to changes in the data path. On the other hand, the global linear trend model makes no allowance for structural change. In this paper we introduce a new model that, as well as encompassing the global linear trend and local linear trend models, allows for a range of "in between" cases. The theoretical properties of the autocovariance and forecast functions for this model suggest that it should be useful when neither a local linear trend nor a global linear trend is appropriate. A comparison of forecasting performance using real time series provides further support for this hypothesis