Discovery of motifs to forecast outlier occurrence in time series

The forecasting process of real-world time series has to deal with especially unexpected values, commonly known as outliers. Outliers in time series can lead to unreliable modeling and poor forecasts. Therefore, the identification of future outlier occurrence is an essential task in time series analysis to reduce the average forecasting error. The main goal of this work is to predict the occurrence of outliers in time series, based on the discovery of motifs. In this sense, motifs will be those pattern sequences preceding certain data marked as anomalous by the proposed metaheuristic in a training set. Once the motifs are discovered, if data to be predicted are preceded by any of them, such data are identified as outliers, and treated separately from the rest of regular data. The forecasting of outlier occurrence has been added as an additional step in an existing time series forecasting algorithm (PSF), which was based on pattern sequence similarities. Robust statistical methods have been used to evaluate the accuracy of the proposed approach regarding the forecasting of both occurrence of outliers and their corresponding values. Finally, the methodology has been tested on six electricity-related time series, in which most of the outliers were properly found and forecasted.