This paper tackles the modelling of large, complex and multivariate time series panels inaprobabilistic setting.

These values are normalized, as noted above, using min-max values from the conditioning range; the prediction range can go below the min and above the max.

Machine learning (ML)-based weather models have rapidly risen to prominence due to their greater accuracy and speed than traditional forecasts based on numerical weather prediction (NWP), recently outperforming traditional ensembles in global probabilistic weather forecasting. This paper presents FGN, a simple, scalable and flexible modeling approach which significantly outperforms the current state-of-the-art models. FGN generates ensembles via learned model-perturbations with an ensemble of appropriately constrained models. It is trained directly to minimize the continuous rank probability score (CRPS) of per-location forecasts. It produces state-of-the-art ensemble forecasts as measured by a range of deterministic and probabilistic metrics, makes skillful ensemble tropical cyclone track predictions, and captures joint spatial structure despite being trained only on marginals.

We introduce the use of Gaussian Processes (GPs) for the probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function and marginalizes it out when making predictions. We couple the latent GP variable with two types of forecast distributions: the negative binomial (NegBinGP) and the Tweedie distribution (TweedieGP). While the negative binomial has already been used in forecasting intermittent time series, this is the first time in which a fully parameterized Tweedie density is used for intermittent time series. We properly evaluate the Tweedie density, which is both zero-inflated and heavy tailed, avoiding simplifying assumptions made in existing models. We test our models on thousands of intermittent count time series. Results show that our models provide consistently better probabilistic forecasts than the competitors. In particular, TweedieGP obtains the best estimates of the highest quantiles, thus showing that it is more flexible than NegBinGP.

Accurate demand forecasting is vital for ensuring reliable access to contraceptive products, supporting key processes like procurement, inventory, and distribution. However, forecasting contraceptive demand in developing countries presents challenges, including incomplete data, poor data quality, and the need to account for multiple geographical and product factors. Current methods often rely on simple forecasting techniques, which fail to capture demand uncertainties arising from these factors, warranting expert involvement. Our study aims to improve contraceptive demand forecasting by combining probabilistic forecasting methods with expert knowledge. We developed a hybrid model that combines point forecasts from domain-specific model with probabilistic distributions from statistical and machine learning approaches, enabling human input to fine-tune and enhance the system-generated forecasts. This approach helps address the uncertainties in demand and is particularly useful in resource-limited settings. We evaluate different forecasting methods, including time series, Bayesian, machine learning, and foundational time series methods alongside our new hybrid approach. By comparing these methods, we provide insights into their strengths, weaknesses, and computational requirements. Our research fills a gap in forecasting contraceptive demand and offers a practical framework that combines algorithmic and human expertise. Our proposed model can also be generalized to other humanitarian contexts with similar data patterns.

Since their introduction by Breiman, Random Forests (RFs) have proven to be useful for both classification and regression tasks. The RF prediction of a previously unseen observation can be represented as a weighted sum of all training sample observations. This nearest-neighbor-type representation is useful, among other things, for constructing forecast distributions (Meinshausen, 2006). In this paper, we consider simplifying RF-based forecast distributions by sparsifying them. That is, we focus on a small subset of nearest neighbors while setting the remaining weights to zero. This sparsification step greatly improves the interpretability of RF predictions. It can be applied to any forecasting task without re-training existing RF models. In empirical experiments, we document that the simplified predictions can be similar to or exceed the original ones in terms of forecasting performance. We explore the statistical sources of this finding via a stylized analytical model of RFs. The model suggests that simplification is particularly promising if the unknown true forecast distribution contains many small weights that are estimated imprecisely.

In Part I, we created an ensemble based on Spherical Fourier Neural Operators. As initial condition perturbations, we used bred vectors, and as model perturbations, we used multiple checkpoints trained independently from scratch. Based on diagnostics that assess the ensemble's physical fidelity, our ensemble has comparable performance to operational weather forecasting systems. However, it requires several orders of magnitude fewer computational resources. Here in Part II, we generate a huge ensemble (HENS), with 7,424 members initialized each day of summer 2023. We enumerate the technical requirements for running huge ensembles at this scale. HENS precisely samples the tails of the forecast distribution and presents a detailed sampling of internal variability. For extreme climate statistics, HENS samples events 4$\sigma$ away from the ensemble mean. At each grid cell, HENS improves the skill of the most accurate ensemble member and enhances coverage of possible future trajectories. As a weather forecasting model, HENS issues extreme weather forecasts with better uncertainty quantification. It also reduces the probability of outlier events, in which the verification value lies outside the ensemble forecast distribution.

Hierarchical time-series forecasting (HTSF) is an important problem for many real-world business applications where the goal is to simultaneously forecast multiple time-series that are related to each other via a hierarchical relation. Recent works, however, do not address two important challenges that are typically observed in many demand forecasting applications at large companies. First, many time-series at lower levels of the hierarchy have high sparsity i.e., they have a significant number of zeros. Most HTSF methods do not address this varying sparsity across the hierarchy. Further, they do not scale well to the large size of the real-world hierarchy typically unseen in benchmarks used in literature. We resolve both these challenges by proposing HAILS, a novel probabilistic hierarchical model that enables accurate and calibrated probabilistic forecasts across the hierarchy by adaptively modeling sparse and dense time-series with different distributional assumptions and reconciling them to adhere to hierarchical constraints. We show the scalability and effectiveness of our methods by evaluating them against real-world demand forecasting datasets. We deploy HAILS at a large chemical manufacturing company for a product demand forecasting application with over ten thousand products and observe a significant 8.5\% improvement in forecast accuracy and 23% better improvement for sparse time-series. The enhanced accuracy and scalability make HAILS a valuable tool for improved business planning and customer experience.