Forecasting Time Series by an Ensemble of Artificial Neural Networks based on transforming the Time Series

Times series forecasting issue can be found in several subject areas as finance and business (e.g. foreign exchange rates, data for prices), industry (energy load and demand), climate and meteorology (e.g. sea surface temperature and El Nio phenomenon), health (e.g. prognosis from medical data) and many others. This paper is focused in univariate time series (x(1), x(2), ..., x(t)), so unknown future values are obtain from k previous (and known) values, i.e. x(t+h) = f(x(t), ..., x(t-k+1)). In order to fit a model between independent variables (present and past values) and dependent variables (future values), Artificial Neural Networks lead to similar or better results than those with statistical techniques, especially for non linear time series. In addition, Ensembles can be applied to outperform the performance of a single model (e.g. a single ANN). In this work, we present an ensemble of Artificial Neural Networks with three elements, were each of them is specialised in one of the three following versions of the time series data: i) raw time series values (i.e. with no modifications); ii) differencing the time series data (computing the difference between consecutive values). The output of the Ensemble merges the answer of the model obtained for each transformation of the time series.