Contextually Enhanced ES-dRNN with Dynamic Attention for Short-Term Load Forecasting

In this paper, we propose a new short-term load forecasting (STLF) model based on contextually enhanced hybrid and hierarchical architecture combining exponential smoothing (ES) and a recurrent neural network (RNN). The model is composed of two simultaneously trained tracks: the context track and the main track. The context track introduces additional information to the main track. It is extracted from representative series and dynamically modulated to adjust to the individual series forecasted by the main track. The RNN architecture consists of multiple recurrent layers stacked with hierarchical dilations and equipped with recently proposed attentive dilated recurrent cells. These cells enable the model to capture short-term, long-term and seasonal dependencies across time series as well as to weight dynamically the input information. The model produces both point forecasts and predictive intervals. The experimental part of the work performed on 35 forecasting problems shows that the proposed model outperforms in terms of accuracy its predecessor as well as standard statistical models and state-of-the-art machine learning models.

STD: A Seasonal-Trend-Dispersion Decomposition of Time Series

The decomposition of a time series is an essential task that helps to understand its very nature. It facilitates the analysis and forecasting of complex time series expressing various hidden components such as the trend, seasonal components, cyclic components and irregular fluctuations. Therefore, it is crucial in many fields for forecasting and decision processes. In recent years, many methods of time series decomposition have been developed, which extract and reveal different time series properties. Unfortunately, they neglect a very important property, i.e. time series variance. To deal with heteroscedasticity in time series, the method proposed in this work -- a seasonal-trend-dispersion decomposition (STD) -- extracts the trend, seasonal component and component related to the dispersion of the time series. We define STD decomposition in two ways: with and without an irregular component. We show how STD can be used for time series analysis and forecasting.

Recurrent Neural Networks for Forecasting Time Series with Multiple Seasonality: A Comparative Study

This paper compares recurrent neural networks (RNNs) with different types of gated cells for forecasting time series with multiple seasonality. The cells we compare include classical long short term memory (LSTM), gated recurrent unit (GRU), modified LSTM with dilation, and two new cells we proposed recently, which are equipped with dilation and attention mechanisms. To model the temporal dependencies of different scales, our RNN architecture has multiple dilated recurrent layers stacked with hierarchical dilations. The proposed RNN produces both point forecasts and predictive intervals (PIs) for them. An empirical study concerning short-term electrical load forecasting for 35 European countries confirmed that the new gated cells with dilation and attention performed best.

Boosted Ensemble Learning based on Randomized NNs for Time Series Forecasting

Time series forecasting is a challenging problem particularly when a time series expresses multiple seasonality, nonlinear trend and varying variance. In this work, to forecast complex time series, we propose ensemble learning which is based on randomized neural networks, and boosted in three ways. These comprise ensemble learning based on residuals, corrected targets and opposed response. The latter two methods are employed to ensure similar forecasting tasks are solved by all ensemble members, which justifies the use of exactly the same base models at all stages of ensembling. Unification of the tasks for all members simplifies ensemble learning and leads to increased forecasting accuracy. This was confirmed in an experimental study involving forecasting time series with triple seasonality, in which we compare our three variants of ensemble boosting. The strong points of the proposed ensembles based on RandNNs are extremely rapid training and pattern-based time series representation, which extracts relevant information from time series.

ES-dRNN with Dynamic Attention for Short-Term Load Forecasting

Short-term load forecasting (STLF) is a challenging problem due to the complex nature of the time series expressing multiple seasonality and varying variance. This paper proposes an extension of a hybrid forecasting model combining exponential smoothing and dilated recurrent neural network (ES-dRNN) with a mechanism for dynamic attention. We propose a new gated recurrent cell -- attentive dilated recurrent cell, which implements an attention mechanism for dynamic weighting of input vector components. The most relevant components are assigned greater weights, which are subsequently dynamically fine-tuned. This attention mechanism helps the model to select input information and, along with other mechanisms implemented in ES-dRNN, such as adaptive time series processing, cross-learning, and multiple dilation, leads to a significant improvement in accuracy when compared to well-established statistical and state-of-the-art machine learning forecasting models. This was confirmed in the extensive experimental study concerning STLF for 35 European countries.

ES-dRNN: A Hybrid Exponential Smoothing and Dilated Recurrent Neural Network Model for Short-Term Load Forecasting

Short-term load forecasting (STLF) is challenging due to complex time series (TS) which express three seasonal patterns and a nonlinear trend. This paper proposes a novel hybrid hierarchical deep learning model that deals with multiple seasonality and produces both point forecasts and predictive intervals (PIs). It combines exponential smoothing (ES) and a recurrent neural network (RNN). ES extracts dynamically the main components of each individual TS and enables on-the-fly deseasonalization, which is particularly useful when operating on a relatively small data set. A multi-layer RNN is equipped with a new type of dilated recurrent cell designed to efficiently model both short and long-term dependencies in TS. To improve the internal TS representation and thus the model's performance, RNN learns simultaneously both the ES parameters and the main mapping function transforming inputs into forecasts. We compare our approach against several baseline methods, including classical statistical methods and machine learning (ML) approaches, on STLF problems for 35 European countries. The empirical study clearly shows that the proposed model has high expressive power to solve nonlinear stochastic forecasting problems with TS including multiple seasonality and significant random fluctuations. In fact, it outperforms both statistical and state-of-the-art ML models in terms of accuracy.

Ensembles of Randomized NNs for Pattern-based Time Series Forecasting

In this work, we propose an ensemble forecasting approach based on randomized neural networks. Improved randomized learning streamlines the fitting abilities of individual learners by generating network parameters in accordance with the data and target function features. A pattern-based representation of time series makes the proposed approach suitable for forecasting time series with multiple seasonality. We propose six strategies for controlling the diversity of ensemble members. Case studies conducted on four real-world forecasting problems verified the effectiveness and superior performance of the proposed ensemble forecasting approach. It outperformed statistical models as well as state-of-the-art machine learning models in terms of forecasting accuracy. The proposed approach has several advantages: fast and easy training, simple architecture, ease of implementation, high accuracy and the ability to deal with nonstationarity and multiple seasonality in time series.

Data-Driven Learning of Feedforward Neural Networks with Different Activation Functions

This work contributes to the development of a new data-driven method (D-DM) of feedforward neural networks (FNNs) learning. This method was proposed recently as a way of improving randomized learning of FNNs by adjusting the network parameters to the target function fluctuations. The method employs logistic sigmoid activation functions for hidden nodes. In this study, we introduce other activation functions, such as bipolar sigmoid, sine function, saturating linear functions, reLU, and softplus. We derive formulas for their parameters, i.e. weights and biases. In the simulation study, we evaluate the performance of FNN data-driven learning with different activation functions. The results indicate that the sigmoid activation functions perform much better than others in the approximation of complex, fluctuated target functions.

Autoencoder based Randomized Learning of Feedforward Neural Networks for Regression

Feedforward neural networks are widely used as universal predictive models to fit data distribution. Common gradient-based learning, however, suffers from many drawbacks making the training process ineffective and time-consuming. Alternative randomized learning does not use gradients but selects hidden node parameters randomly. This makes the training process extremely fast. However, the problem in randomized learning is how to determine the random parameters. A recently proposed method uses autoencoders for unsupervised parameter learning. This method showed superior performance on classification tasks. In this work, we apply this method to regression problems, and, finding that it has some drawbacks, we show how to improve it. We propose a learning method of autoencoders that controls the produced random weights. We also propose how to determine the biases of hidden nodes. We empirically compare autoencoder based learning with other randomized learning methods proposed recently for regression and find that despite the proposed improvement of the autoencoder based learning, it does not outperform its competitors in fitting accuracy. Moreover, the method is much more complex than its competitors.

Randomized Neural Networks for Forecasting Time Series with Multiple Seasonality

This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating network parameters in accordance with the data and target function features. A pattern-based representation of time series makes the proposed approach useful for forecasting time series with multiple seasonality. In the simulation study, we evaluate the performance of the proposed models and find that they can compete in terms of forecasting accuracy with fully-trained networks. Extremely fast and easy training, simple architecture, ease of implementation, high accuracy as well as dealing with nonstationarity and multiple seasonality in time series make the proposed model very attractive for a wide range of complex time series forecasting problems.