Fuzzy Long Term Forecasting through Machine Learning and Symbolic Representations of Time Series

Abstract

Time series forecasting is often done “one step ahead” with statistical models or numerical machine learning algorithms. It is possible to extend those predictive models to a few steps ahead and iterate the predictions thus allowing further forecasting. However, it is not possible to do this for thousands of data points because cumulative error tends to make the long term forecasting unreliable. Such uncertainty can be conveied by the use of fuzzy forecasting where the forecasted value is a fuzzy set rather than a number. The end-user can only appreciate the uncertainty of the forecast if the forecasting model is easy to understand. Contrary to common “black-box” models, we use symbolic machine learning on symbolic representations of time-series. In this paper, we tackle the real-world issue of forecasting electric load for one year, sampled every ten minutes, with data available for the past few years. In this context, future values are not only related to their short term previous values, but also to temporal attributes (the day of the week, holidays ...). We use a symbolic machine learning algorithm (decision tree) to extract this kind of knowledge and predict future pattern occurences. Those patterns are learnt when building a symbolic representation of the time series, by clustering episodes showing similar patterns and making the cluster a symbolic attribute of the episodes. Intra-class variations result in forecasting uncertainty that we model through fuzzy prototypes. Those prototypes are then used to construct a fuzzy forecasting easily understood by the end-user.