# Simulating Intraday Electricity Consumption with ForGAN
## 1 Introduction  
A time series can be regarded as a sequence of correlated experiments where the result of the current experiment has an influence on the distribution of the following experiment's result. Therefore, observing a time series needs time. Thus, data coming from a time series with a realistic length are typically sparse. This also makes the two classical tasks in the application of time series modeling, prediction of future values (_forecasting_) and simulation of different future realizations (_generation of additional data_), challenging. The traditional literature on time series models such as autoregressive, ARIMA-type or regression-based models is mostly focused on prediction (see, e.g., [1,2] for the traditional time series approach). For this, an explicit functional relation between past values and the next value of the time series is assumed. Uncertainty typically enters via an additive error with zero expectation. Having estimated the parameters that determine the above-mentioned functional relation, the prediction of future values (given the past data) is uniquely determined. These methods often rely on assumptions such as linearity and stationarity, and they typically model uncertainty as Gaussian noise. As a result, they are poorly suited for capturing non-linear dependencies or generating diverse future scenarios, particularly when data are sparse or exhibit seasonal patterns. Predicting the next value is also the typical task, even in state-of-the-art time series applications related to electricity consumption, production or \(CO_{2}\) emissions (see, e.g., [3] for regression-based forecasts or [4] for a combination of periodic function approaches). In contrast to these classical approaches, the focus here is not on the best prediction but on the approximation of the next element's conditional distribution. This approach allows us to simulate a whole set of possible next elements for the same past data. No model is assumed for the time series evolution; instead, a purely data-based algorithm is provided. However, when the full conditional distribution of the next value in a time series is needed, the traditional methods fail. They either typically generate the same value (given the past observations) or use an artificial model-based distribution, with the generated output deviating significantly from the true conditional distribution of the next value in the time series. However, when strategical decisions have to be taken, such as an enlargement or a partial reduction in the production capacity, it is important that not only the most likely next values are known but that the full underlying conditional distribution is also found. At this point, so-called generative networks become relevant. Recent advancements in generative models, particularly generative adversarial networks (GANs), offer a promising approach for generating realistic synthetic data samples that closely follow the distribution underlying true data. This allows for an augmentation of a given dataset, helping the model to better capture complex patterns and improve the realism of simulated outcomes. GANs have achieved notable results in generating realistic samples in a variety of problem areas, such as producing real-looking images of human faces [5], translating one image to another (for example, photos of summer to winter [6] or day to night [7]), and 3D image generation [8]. Other research areas encompass speech synthesis [9] and video generation [10]. Although many of the above applications of GANs focus on static data, the focus here is on generating time series data. This shift in focus from static to sequential data requires architectures that can learn temporal data dependencies effectively. To describe the desired task and to demonstrate the application of our new method, the example of generating the next sequence of total electricity consumption per 15 min in Germany is considered. This contribution focuses on ForGAN (see [11]), a conditional GAN (cGAN) specifically designed for time series simulations.