A successive filtering technique for identifying long-term trends

The most reliable component of a time series, for forecasting purposes, is the shape of the long-term trend. However, the presence of cycles makes it difficult to identify and predict the changes in such trends. While up to now emphasis has been given in identifying and measuring cyclical behaviour, this paper presents a technique that aims at removing cyclical effects from the long-term trends. This technique is based on a transformation that is successively applied on the original time series. Each time the transformation is applied, an observation is selected and replaced by the average of its adjacent observations. This results in the elimination of the cyclical component. Independently of their depth, the cycles are being removed in ascending order relatively to their length. This leads to ‘brushing off’ the long-term trends from any cyclical effects. A specialized software has been developed in Pascal. The proposed technique was applied in a set of time series from the M2- and M-competition and the results are presented in this paper.