With the advent of Big Data, nowadays in many applications databases containing large quantities of similar time series are available. Forecasting time series in these domains with traditional univariate forecasting procedures leaves great potentials for producing accurate forecasts untapped. Recurrent neural networks (RNNs), and in particular Long Short-Term Memory (LSTM) networks, have proven recently that they are able to outperform state-of-the-art univariate time series forecasting methods in this context when trained across all available time series. However, if the time series database is heterogeneous, accuracy may degenerate, so that on the way towards fully automatic forecasting methods in this space, a notion of similarity between the time series needs to be built into the methods. To this end, we present a prediction model that can be used with different types of RNN models on subgroups of similar time series, which are identified by time series clustering techniques. We assess our proposed methodology using LSTM networks, a widely popular RNN variant. Our method achieves competitive results on benchmarking datasets under competition evaluation procedures. In particular, in terms of mean sMAPE accuracy, it consistently outperforms the baseline LSTM model and outperforms all other methods on the CIF2016 forecasting competition dataset.
The powerful data-driven self-adaptability and model generalizability enable NNs to uncover complex relationships among samples and perform predictions on new observations of a population, without being constrained by assumptions regarding the underlying data generating process of a dataset. These promising characteristics are further strengthened by the universal function approximation properties that NNs possess . Therefore, NNs are popular for classification and regression, and also in time series forecasting when external regressors and additional knowledge is available. In pure univariate time series forecasting, over the past two decades, NN architectures have been advocated as a strong alternative to traditional statistical forecasting methods . Researchers have been increasingly drawing their interest towards developing and applying different NN models for time series forecasting. This includes multi-layer perceptrons (MLP), GRNNs, ensemble architectures, RNNs, ESNs and LSTMs, while MLPs are being the most widely used NN variant for time series forecasting thus far. For a detailed description of the MLP architecture and its widespread applications employed in time series forecasting see @cite_4 .
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Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.