Forecasting, Volume 5, Issue 3 (September 2023) – 5 articles

In recent years, there has been a noticeable shift towards electric mobility and an increasing emphasis on integrating renewable energy sources. Consequently, batteries and their management have been prominent in this context. A vital aspect of the BMS revolves around accurately determining the battery pack’s SOC. Notably, the advent of advanced microcontrollers and the availability of extensive datasets have contributed to the growing popularity and practicality of data-driven methodologies. This study examines the developments in SOC estimation over the past half-decade, explicitly focusing on data-driven estimation techniques. It comprehensively assesses the performance of each algorithm, considering the type of battery and various operational conditions. Additionally, intricate details concerning the models’ hyperparameters, including the number of layers, type of optimiser, and neuron, are provided for thorough examination. Most of the models analysed in the paper demonstrate strong performance, with both the MAE and RMSE for the estimation of SOC hovering around 2% or even lower. Full article

Assessing the training process of artificial neural networks (ANNs) is vital for enhancing their performance and broadening their applicability. This paper employs the Monte Carlo simulation (MCS) technique, integrated with a stopping criterion, to construct the probability distribution of the learning error of an ANN designed for short-term forecasting. The training and validation processes were conducted multiple times, each time considering a unique random starting point, and the subsequent forecasting error was calculated one step ahead. From this, we ascertained the probability of having obtained all the local optima. Our extensive computational analysis involved training a shallow feedforward neural network (FFNN) using wind power and load demand data from the transmission systems of the Netherlands and Germany. Furthermore, the analysis was expanded to include wind speed prediction using a long short-term memory (LSTM) network at a site in Spain. The improvement gained from the FFNN, which has a high probability of being the global optimum, ranges from 0.7% to 8.6%, depending on the forecasting variable. This solution outperforms the persistent model by between 5.5% and 20.3%. For wind speed predictions using an LSTM, the improvement over an average-trained network stands at 9.5%, and is 6% superior to the persistent approach. These outcomes suggest that the advantages of exhaustive search vary based on the problem being analyzed and the type of network in use. The MCS method we implemented, which estimates the probability of identifying all local optima, can act as a foundational step for other techniques like Bayesian model selection, which assumes that the global optimum is encompassed within the available hypotheses. Full article

ChatGPT, a state-of-the-art large language model (LLM), is revolutionizing the AI field by exhibiting humanlike skills in a range of tasks that include understanding and answering natural language questions, translating languages, writing code, passing professional exams, and even composing poetry, among its other abilities. ChatGPT has gained an immense popularity since its launch, amassing 100 million active monthly users in just two months, thereby establishing itself as the fastest-growing consumer application to date. This paper discusses the reasons for its success as well as the future prospects of similar large language models (LLMs), with an emphasis on their potential impact on forecasting, a specialized and domain-specific field. This is achieved by first comparing the correctness of the answers of the standard ChatGPT and a custom one, trained using published papers from a subfield of forecasting where the answers to the questions asked are known, allowing us to determine their correctness compared to those of the two ChatGPT versions. Then, we also compare the responses of the two versions on how judgmental adjustments to the statistical/ML forecasts should be applied by firms to improve their accuracy. The paper concludes by considering the future of LLMs and their impact on all aspects of our life and work, as well as on the field of forecasting specifically. Finally, the conclusion section is generated by ChatGPT, which was provided with a condensed version of this paper and asked to write a four-paragraph conclusion. Full article

Mathematical aggregation of probabilistic expert judgments often involves weighted linear combinations of experts’ elicited probability distributions of uncertain quantities. Experts’ weights are commonly derived from calibration experiments based on the experts’ performance scores, where performance is evaluated in terms of the calibration and the informativeness of the elicited distributions. This is referred to as Cooke’s method, or the classical model (CM), for aggregating probabilistic expert judgments. The performance scores are derived from experiments, so they are uncertain and, therefore, can be represented by random variables. As a consequence, the experts’ weights are also random variables. We focus on addressing the underlying uncertainty when calculating experts’ weights to be used in a mathematical aggregation of expert elicited distributions. This paper investigates the potential of applying an empirical Bayes development of the James–Stein shrinkage estimation technique on the CM’s weights to derive shrinkage weights with reduced mean squared errors. We analyze 51 professional CM expert elicitation studies. We investigate the differences between the classical and the (new) shrinkage CM weights and the benefits of using the new weights. In theory, the outcome of a probabilistic model using the shrinkage weights should be better than that obtained when using the classical weights because shrinkage estimation techniques reduce the mean squared errors of estimators in general. In particular, the empirical Bayes shrinkage method used here reduces the assigned weights for those experts with larger variances in the corresponding sampling distributions of weights in the experiment. We measure improvement of the aggregated judgments in a cross-validation setting using two studies that can afford such an approach. Contrary to expectations, the results are inconclusive. However, in practice, we can use the proposed shrinkage weights to increase the reliability of derived weights when only small-sized experiments are available. We demonstrate the latter on 49 post-2006 professional CM expert elicitation studies. Full article

This paper proposes a new hybrid model to forecast electricity market prices up to four days ahead. The components of the proposed model are combined in two dimensions. First, on the “vertical” dimension, long short-term memory (LSTM) neural networks and extreme gradient boosting (XGBoost) models are stacked up to produce supplementary price forecasts. The final forecasts are then picked depending on how the predictions compare to a price spike threshold. On the “horizontal” dimension, five models are designed to extend the forecasting horizon to four days. This is an important requirement to make forecasts useful for market participants who trade energy and ancillary services multiple days ahead. The horizontally cascaded models take advantage of the availability of specific public data for each forecasting horizon. To enhance the forecasting capability of the model in dealing with price spikes, we deploy a previously unexplored input in the proposed methodology. That is, to use the recent variations in the output power of thermal units as an indicator of unplanned outages or shift in the supply stack. The proposed method is tested using data from Alberta’s electricity market, which is known for its volatility and price spikes. An economic application of the developed forecasting model is also carried out to demonstrate how several market players in the Alberta electricity market can benefit from the proposed multi-day ahead price forecasting model. The numerical results demonstrate that the proposed methodology is effective in enhancing forecasting accuracy and price spike detection. Full article