Forecasting of curves using a Kohonen classification

Abstract

This paper addresses an extensively studied problem, which is a particular case of long‐term forecasting. In many practical situations, one has to predict a complete curve, i.e. the set of the 24 hourly values for the next day, of all the daily values for the next month or for the next year. For example, it is the case if the matter is to forecast the daily half‐hour electricity consumption. Many methods have been developed, standard linear methods (e.g. ARIMA) as well as neural ones. In this paper we present a very simple method that we call the K‐method. We assume the forecasting problem can be split up into three subproblems: the forecast of the mean (level of the values), of the standard deviation (scattering) and of the normalized profile (which essentially represents the shape). The profiles are classified using a Kohonen map with the neighbourhood preservation property and the mean and variance are fitted using any convenient short‐term forecasting method. Then, for some future curve, a strategy is defined in order to compute its expected normalized profile, the mean and the variance are forecast and the expected curve is computed. This method is low computation time consuming and is easy to develop. Two applications are presented: an example using artificial data and the prediction of the daily half‐hour electrical power curves in France. Copyright © 1998 John Wiley & Sons, Ltd.

Theoretical aspects of the SOM algorithm

“…In [15] and [17], an application to forecasting is presented from a previous classification by a SOM algorithm.…”

Exploratory analysis of functional data via clustering and optimal segmentation

“…A classical solution for multivariate data consists in using a prototype based clustering approach: each cluster is summarized by its prototype. Standard clustering methods such as K means and Self Organizing Map have been adapted to functional data and could be used to implement this solution [1,6,8,29]. Another possibility comes from the symbolization approaches in which a time series is represented by a sequence of symbols.…”

Neural Networks for Complex Data

“…An alternative solution is explored in [12]. It consists in forecasting separately, on the one hand, the mean and variance of the time series on next slow time scale step (that is, on the next j), and on the other hand, the profile of the fast time scale.…”

“…Finally, a weighted average of the matching prototypes is computed and rescaled according to µ and σ . As shown in [12] this technique enables both some stable and meaningful full day predictions, while integrating non numerical metadata.…”