Time series forecasting is one of the challenging problems for humankind. Traditional forecasting methods using mean regression models have severe shortcomings in reflecting real-world fluctuations. While new probabilistic methods rush to rescue, they fight with technical difficulties like quantile crossing or selecting a prior distribution. To meld the different strengths of these fields while avoiding their weaknesses as well as to push the boundary of the state-of-the-art, we introduce ForGAN – one step ahead probabilistic forecasting with generative adversarial networks. ForGAN utilizes the power of the conditional generative adversarial network to learn the data generating distribution and compute probabilistic forecasts from it. We argue how to evaluate ForGAN in opposition to regression methods. To investigate probabilistic forecasting of ForGAN, we create a new dataset and demonstrate our method abilities on it. This dataset will be made publicly available for comparison. Furthermore, we test ForGAN on two publicly available datasets, namely Mackey-Glass dataset mackey1977oscillation and Internet traffic dataset (A5M) cortez2012multi where the impressive performance of ForGAN demonstrate its high capability in forecasting future values.

The contribution of this paper is two-fold. First, we present ProbCast—a novel probabilistic model for multivariate time-series forecasting. We employ a conditional GAN framework to train our model with adversarial training. Second, we propose a framework that lets us transform a deterministic model into a probabilistic one with improved performance. The motivation of the framework is to either transform existing highly accurate point forecast models to their probabilistic counterparts or to train GANs stably by selecting the architecture of GAN’s component carefully and efficiently. We conduct experiments over two publicly available datasets—an electricity consumption dataset and an exchange-rate dataset. The results of the experiments demonstrate the remarkable performance of our model as well as the successful application of our proposed framework.

The recent developments in the machine-learning domain have enabled the development of complex multivariate probabilistic forecasting models. To evaluate the predictive power of these complex methods, it is pivotal to have a precise evaluation method to gauge the performance and predictability power of these complex methods. To do so, several evaluation metrics have been proposed in the past (such as the energy score, Dawid–Sebastiani score, and variogram score); however, these cannot reliably measure the performance of a probabilistic forecaster. Recently, CRPS-Sum has gained a lot of prominence as a reliable metric for multivariate probabilistic forecasting. This paper presents a systematic evaluation of CRPS-Sum to understand its discrimination ability. We show that the statistical properties of target data affect the discrimination ability of CRPS-Sum. Furthermore, we highlight that CRPS-Sum calculation overlooks the performance of the model on each dimension. These flaws can lead us to an incorrect assessment of model performance. Finally, with experiments on real-world datasets, we demonstrate that the shortcomings of CRPS-Sum provide a misleading indication of the probabilistic forecasting performance method. We illustrate that it is easily possible to have a better CRPS-Sum for a dummy model, which looks like random noise, in comparison to the state-of-the-art method.

Despite recent breakthroughs in the domain of implicit generative models, the task of evaluating these models remains a challenging task. With no single metric to assess overall performance, various existing metrics only offer partial information. This issue is further compounded for unintuitive data types such as time series, where manual inspection is infeasible. This deficiency hinders the confident application of modern implicit generative models on time series data. To alleviate this problem, we propose two new metrics, the InceptionTime Score (ITS) and the Fréchet InceptionTime Distance (FITD), to assess the quality of class-conditional generative models on time series data. We conduct extensive experiments on 80 different datasets to study the discriminative capabilities of proposed metrics alongside two existing evaluation metrics: Train on Synthetic Test on Real (TSTR) and Train on Real Test on Synthetic (TRTS). Our evaluations reveal that the proposed assessment evaluation metrics, i.e., ITS and FITD in combination with TSTR, can accurately assess class-conditional generative model performance and detect common issues in implicit generative models. Our findings suggest that the proposed evaluation framework can be a valuable tool for confidently applying modern implicit generative models in time series analysis.

This paper introduces VAEneu, a novel autoregressive method for multistep ahead univariate probabilistic time series forecasting, designed to address the challenges of generating sharp and well-calibrated probabilistic forecasts without assuming a specific parametric form for the predictive distribution. VAEneu leverages the Conditional VAE framework and optimizes the likelihood of the predictive distribution using the Continuous Ranked Probability Score (CRPS), a strictly proper scoring rule, as the loss function. This approach enables the model to learn flexible, sharp, and well-calibrated predictive distributions without the need for a tractable likelihood function. In a comprehensive empirical study, VAEneu is rigorously benchmarked against 12 baseline models across 12 datasets, demonstrating superior performance in both forecasting accuracy and uncertainty quantification. VAEneu provides a valuable tool for quantifying future uncertainties, and our extensive empirical study lays the foundation for future comparative studies for univariate multistep ahead probabilistic forecasting.