Geometrical Realization for Time Series Forecasting

This research primarily focuses on tackling the challenge of forecasting univariate time series. Existing methods for training forecasting models range from traditional statistical models to domain-specific algorithms, and more recently deep neural network models typically rely on raw time series observations, with alternative representations like higher-dimensional embedding used mainly for auxiliary analyses such as Topological Data Analysis (TDA). In contrast to conventional time series analysis methods, this study explores the impact of higher-dimensional embedding as a primary data representation. Leveraging this higher-dimensional embedding, we introduce a geometrical realization model that captures crucial data points of the embedding representation. Subsequently, we propose a deep neural network model inspired by N-BEATS, incorporating a TDA model, an attention model, and a convolutional neural network (CNN) model in parallel as sub-modules alongside the geometrical realization model. To assess the efficacy of the proposed model, we conduct evaluations on diverse time series datasets spanning various domains, including electricity load demands and M4 competition datasets. Furthermore, we conduct an ablation study to analyze the specific contributions of each sub-module towards the final predictions.