We present an online method for guaranteeing calibration of quantile forecasts at multiple quantile levels simultaneously. A sequence of $α$-level quantile forecasts is calibrated if the forecasts are larger than the target value at an $α$-fraction of time steps. We introduce a lightweight method called Multi-Level Quantile Tracker (MultiQT) that wraps around any existing point or quantile forecaster to produce corrected forecasts guaranteed to achieve calibration, even against adversarial distribution shifts, while ensuring that the forecasts are ordered -- e.g., the 0.5-level quantile forecast is never larger than the 0.6-level forecast. Furthermore, the method comes with a no-regret guarantee that implies it will not worsen the performance of an existing forecaster, asymptotically, with respect to the quantile loss. In experiments, we find that MultiQT significantly improves the calibration of real forecasters in epidemic and energy forecasting problems.

Obtaining accurate probabilistic energy forecasts and making effective decisions amid diverse uncertainties are routine challenges in future energy systems. This paper presents the winning solution of team GEB, which ranked 3rd in trading, 4th in forecasting, and 1st among student teams in the IEEE Hybrid Energy Forecasting and Trading Competition 2024 (HEFTCom2024). The solution provides accurate probabilistic forecasts for a wind-solar hybrid system, and achieves substantial trading revenue in the day-ahead electricity market. Key components include: (1) a stacking-based approach combining sister forecasts from various Numerical Weather Predictions (NWPs) to provide wind power forecasts, (2) an online solar post-processing model to address the distribution shift in the online test set caused by increased solar capacity, (3) a probabilistic aggregation method for accurate quantile forecasts of hybrid generation, and (4) a stochastic trading strategy to maximize expected trading revenue considering uncertainties in electricity prices. This paper also explores the potential of end-to-end learning to further enhance the trading revenue by shifting the distribution of forecast errors. Detailed case studies are provided to validate the effectiveness of these proposed methods. Code for all mentioned methods is available for reproduction and further research in both industry and academia.

--Cryptocurrency markets are characterized by extreme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for capturing the full spectrum of potential volatility outcomes, underscoring the importance of probabilistic approaches. T o address this limitation, this paper introduces probabilistic forecasting methods that leverage point forecasts from a wide range of base models, including statistical (HAR, GARCH, ARFIMA) and machine learning (e.g. LASSO, SVR, MLP, Random Forest, LSTM) algorithms, to estimate conditional quantiles of cryp-tocurrency realized variance. T o the best of our knowledge, this is the first study in the literature to propose and systematically evaluate probabilistic forecasts of variance in cryptocurrency markets based on predictions derived from multiple base models. Our empirical results for Bitcoin demonstrate that the Quantile Estimation through Residual Simulation (QRS) method, particularly when applied to linear base models operating on log-transformed realized volatility data, consistently outperforms more sophisticated alternatives. Additionally, we highlight the robustness of the probabilistic stacking framework, providing comprehensive insights into uncertainty and risk inherent in cryptocurrency volatility forecasting. This research fills a significant gap in the literature, contributing practical probabilistic forecasting methodologies tailored specifically to cryptocurrency markets. Probabilistic forecasting of cryptocurrency volatility is essential due to the considerable uncertainty and frequent occurrence of extreme price movements in cryptocurrency markets. Unlike traditional point forecasts, probabilistic methods estimate the entire conditional distribution (or its fine-grained approximation using densely spaced quantiles) of future volatility, thereby capturing the full range of potential outcomes and significantly improving risk assessment and decision-making in these highly unpredictable markets. Despite these clear benefits, probabilistic forecasting methods remain relatively scarce in the cryptocurrency volatility literature.

Despite significant advancements in time series forecasting, accurate modeling of time series with strong heterogeneity in magnitude and/or sparsity patterns remains challenging for state-of-the-art deep learning architectures. We identify several factors that lead existing models to systematically underperform on low-magnitude and sparse time series, including loss functions with implicit biases toward high-magnitude series, training-time sampling methods, and limitations of time series encoding methods. SPADE-S is a robust forecasting architecture that significantly reduces magnitude- and sparsity-based systematic biases and improves overall prediction accuracy. Empirical results demonstrate that SPADE-S outperforms existing state-of-the-art approaches across a diverse set of use cases in demand forecasting. In particular, we show that, depending on the quantile forecast and magnitude of the series, SPADE-S can improve forecast accuracy by up to 15%. This results in P90 overall forecast accuracy gains of 2.21%, 6.58%, and 4.28%, and P50 forecast accuracy gains of 0.92%, 0.77%, and 1.95%, respectively, for each of three distinct datasets, ranging from 3 million to 700 million series, from a large online retailer.

We introduce AutoGluon-TimeSeries - an open-source AutoML library for probabilistic time series forecasting. Focused on ease of use and robustness, AutoGluon-TimeSeries enables users to generate accurate point and quantile forecasts with just 3 lines of Python code. Built on the design philosophy of AutoGluon, AutoGluon-TimeSeries leverages ensembles of diverse forecasting models to deliver high accuracy within a short training time. AutoGluon-TimeSeries combines both conventional statistical models, machine-learning based forecasting approaches, and ensembling techniques. In our evaluation on 29 benchmark datasets, AutoGluon-TimeSeries demonstrates strong empirical performance, outperforming a range of forecasting methods in terms of both point and quantile forecast accuracy, and often even improving upon the best-in-hindsight combination of prior methods.

This paper develops probabilistic PV forecasters by taking advantage of recent breakthroughs in deep learning. It tailored forecasting tool, named encoder-decoder, is implemented to compute intraday multi-output PV quantiles forecasts to efficiently capture the time correlation. The models are trained using quantile regression, a non-parametric approach that assumes no prior knowledge of the probabilistic forecasting distribution. The case study is composed of PV production monitored on-site at the University of Li\`ege (ULi\`ege), Belgium. The weather forecasts from the regional climate model provided by the Laboratory of Climatology are used as inputs of the deep learning models. The forecast quality is quantitatively assessed by the continuous ranked probability and interval scores. The results indicate this architecture improves the forecast quality and is computationally efficient to be incorporated in an intraday decision-making tool for robust optimization.

This paper addresses the energy management of a grid-connected renewable generation plant coupled with a battery energy storage device in the capacity firming market, designed to promote renewable power generation facilities in small non-interconnected grids. A recently developed deep learning model known as normalizing flows is used to generate quantile forecasts of renewable generation. They provide a general mechanism for defining expressive probability distributions, only requiring the specification of a base distribution and a series of bijective transformations. Then, a probabilistic forecast-driven strategy is designed, modeled as a min-max-min robust optimization problem with recourse, and solved using a Benders decomposition. The convergence is improved by building an initial set of cuts derived from domain knowledge. Robust optimization models the generation randomness using an uncertainty set that includes the worst-case generation scenario and protects this scenario under the minimal increment of costs. This approach improves the results over a deterministic approach with nominal point forecasts by finding a trade-off between conservative and risk-seeking policies. Finally, a dynamic risk-averse parameters selection strategy based on the quantile forecasts distribution provides an additional gain. The case study uses the photovoltaic generation monitored on-site at the University of Li\`ege (ULi\`ege), Belgium.

We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is expanded from a set of fixed quantiles to the whole Quantile Function by a univariate mapping from a latent uniform distribution to the target distribution. Then the multivariate case is solved by learning such quantile functions for each dimension's marginal distribution, followed by estimating a conditional Copula to associate these latent uniform random variables. The quantile functions and copula, together defining the joint predictive distribution, can be parameterized by a single implicit generative Deep Neural Network.

The Tangent Works team participated in GEFCom 2017 to test its automatic model building strategy for time series known as Tangent Information Modeller (TIM). Model building using TIM combined with historical temperature shuffling resulted in winning the competition. This strategy involved one remaining degree of freedom, a decision on using a trend variable. This paper describes our modelling efforts in the competition, and furthermore outlines a fully automated scenario where the decision on using the trend variable is handled by TIM. The results show that such a setup would also win the competition.

We present a simple quantile regression-based forecasting method that was applied in a probabilistic load forecasting framework of the Global Energy Forecasting Competition 2017 (GEFCom2017). The hourly load data is log transformed and split into a long-term trend component and a remainder term. The key forecasting element is the quantile regression approach for the remainder term that takes into account weekly and annual seasonalities such as their interactions. Temperature information is only used to stabilize the forecast of the long-term trend component. Public holidays information is ignored. Still, the forecasting method placed second in the open data track and fourth in the definite data track with our forecasting method, which is remarkable given simplicity of the model. The method also outperforms the Vanilla benchmark consistently.