Problems of points of inflection in trend functions as described by a model for the forecast of brand shares
✍ Scribed by Werner Kroeber-Riel; Sighard Roloff
- Publisher
- Springer US
- Year
- 1973
- Tongue
- English
- Weight
- 443 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0040-5833
No coin nor oath required. For personal study only.
✦ Synopsis
Trends often have special points of uncertainty (surprises) which make forecasts by trend extrapolation impossible. Such points of uncertainty are found especially at points of inflection of functions. In many cases it will be possible to decompose the trend to be forecast into two or more (causal) time series which have no points of inflection. By extrapolating these individual time series it will then be possible to predict the trajectory of the trend function inclusive of the point of inflection. This method is represented and critically discussed by means of an example for the forecast of a brand share.
1. FORECASTING BY EXTRAPOLATION: THE SIGNIFICANCE OF POINTS OF INFLECTION AND OF DECOMPOSITION OF FUNCTIONS
Mathematical forecasting models have taken on increasing importance in economic and social sciences. The development of such models helps to increase the exactness of forecasts.
All forecasting (predictive) inferences are inductive, i.e. uncertain, inferences. The credibility of these inferences depends on the one hand on the formal method of inference -as e.g. extrapolation or analogyand on the other hand is dependent on available empirical data.
The following article is concerned with the formal methods of forecasting: with decomposition of functions which are used for extrapolation. Extrapolation helps to extend an empirically derived trend of previous (past) values into the future. When using the term 'trend' in this article, we generally refer to a time series of some parameter (Ayres) 1. When extrapolating, it is necessary to start from the assumption that the environmental conditions underlying the trend will not change basically; one may well say with Kahn 2 that no surprises should occur. For extrapolating trends one often uses mathematical functions: existing time series are to be approximated as exactly as possible through the values of the functions used. With the help of such functions it will be possible to calculate the values to be forecasted that have not been observed yet.