A temporal-window framework for modelling and forecasting time series

Abstract

Time series have become a valuable source of study in many areas, mainly because it encapsulates some underlying time-index variables. A significant part of these studies is dedicated to fit a single model to the past data to forecast future values of the series. However, single models may not be able to adequately fit local patterns; that is, particular and eventually recurrent variations dynamically incorporated in the series as time evolves. This temporal-window oriented paradigm has been at the vanguard of time series modelling and forecasting exercises. The present paper proposes a simple local-pattern oriented system to model and forecast time series. Our approach involves three steps: (i) the time series is split into k subsets in such a way that each subset may intercept its neighbours; (ii) each subset is modelled, considering lags according to confidence intervals of the auto-correlation function; and (iii) pattern recognition of the target values of the time series in relation to the modelled subsets, via dynamic time warping. The usefulness of the proposed framework is illustrated by modelling and forecasting real-world time series. Evaluation metrics were adopted to compare the proposed approach with multilayer perceptron neural networks and support vector regression predictors. The results provided by published models are also taken into account and it was found that the proposed system presented better performance than the compared models in the experiments.