# Probabilistic Forecasting of Electricity Demand Incorporating Mobility Data
## 1 Introduction

Table 1: Energy forecast accuracy (percentage error) in Australia (AEMO report 2022). Figure 1: Comparison of electricity demand patterns from February to March 2020–2022. The conventional deterministic forecasting (point prediction) methods provide a single expected value, which cannot incorporate the uncertainty information of the forecasting results [7]. In this context, an emerging method known as probabilistic forecasting can make effective inductive reasoning and therefore is more efficient for decision-making under dynamic scenarios [8]. EDF has been extensively studied, and numerous methods have been developed. However, earlier studies of EDF are mostly conducted during regular operations utilizing point forecasts and rarely address the uncertainties caused by any unprecedented events. EDFs are generally classified into two main categories: the statistical approaches and the artificial intelligence (AI) (machine learning) approaches [7]. Since electricity demand is affected by different independent variables such as weather/meteorological factors, statistical approaches which are based on linear models, such as exponential smoothing [7; 8], multiple linear regression models (MLR), generalized autoregressive conditional heteroskedasticity (GARCH) [9], and autoregressive moving average (ARMA), are unable to account for the nonlinearity, non-stationarity, and randomness of time series data [9; 10]. As shown in [9], GARCH models may capture a few aspects of uncertainty but not the volatile properties of time series. Meanwhile, AI-based approaches, such as support vector regression (SVR) [11; 12] and neural network (NN) methods [13; 14], have been used in data analysis, pattern recognition, and EDF with accurate values. SVR is a complex computation involving a large dataset. In contrast, NN models are popular since they can simulate complicated nonlinear relationships. In addition, hybrid models [15; 16; 17] that combine the benefits of single models are gaining popularity for increasing forecast accuracy and resilience. The above-mentioned NN-based parametric methods often require a considerable quantity of data to discover relative patterns from samples due to their various parameters [13]. Given the limited amount of data during anomalous events, direct NN application is not recommended. The above-listed time series approaches are all part of the point forecasting methods that predict a single expected value in look-ahead times to guide decision-making. However, earlier studies of EDF [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17] were mostly conducted during regular operations utilizing point forecasts and rarely addressed the inherent uncertainties caused by unprecedented events such as pandemics. In contrast, a probabilistic forecast estimates the respective probabilities for all the possible future outcomes of a random variable concerning energy uncertainty, which is essential for making better decisions [8; 18]. Three broad types of probabilistic forecasting methods have been developed: (1) input scenario based with simulated predictors [19], (2) interval construction and probabilistic forecasting models [20; 21; 22; 23], and (3) post-processing through residual simulation [24; 25]. Each of these can give a probabilistic result in the form of quantiles, intervals, or density functions [7]. Nevertheless, probabilistic forecasting approaches generally require a lot of data for training [8], making them inappropriate for EDF during unusual events when only a small sample of data is available. Gaussian process regression (GPR), a non-parametric method based on Bayesian theory, is preferable to parameterized methods for probabilistic regression analysis with a small number of training samples. [26]. In addition, GPR makes it possible to quantify the uncertainty of the forecasted values, which is extremely useful for security planning and operation of the system in safety-critical fields, such as energy systems [27].