# Hybrid Load Forecasting Using Gaussian Process Regression and Novel Residual Prediction
###### Abstract  
Short-term electricity load forecasting has attracted considerable attention as a result of the crucial role that it plays in power systems and electricity markets. This paper presents a novel hybrid forecasting method that combines an autoregressive model with Gaussian process regression. Mixed-user, hourly, historical data are used to train, validate, and evaluate the model. The empirical wavelet transform was used to preprocess the data. Among the perturbing factors, the most influential predictors that were recorded were the weather factors and day type. The developed methodology is upgraded using a novel closed-loop algorithm that uses the forecasting values and influential factors to predict the residuals. Most performance indicators that are computed indicate that forecasting the residuals actually improves the method's precision, decreasing the mean absolute percentage error from 5.04% to 4.28%. Measured data are used to validate the effectiveness of the presented approach, making it a suitable tool for use in load forecasting by utility companies. energy forecasting; Gaussian process regression; machine learning models; empirical wavelet transform; residuals prediction 202020103900000000000000000000000000000000000000000000000  
consumption. Forecasting methods may essentially be classified as follows: very short-term load forecasting (a few minutes ahead to a several hours), short-term (one day ahead to one week ahead), medium-term load forecasting (ranging from one month to one year), and long-term load forecasting (more than one year) [2]. Short-term predictions are used in demand and supply management and to balance electricity generation [3], transmission, distribution and use on different scales [4]. Another aspect of load forecasting in the context of the energy sector is the integration of RES into the power grid [5]. The use of a high-quality forecasting model may increase the impact of renewable sources [6]. In terms of energy management, load forecasting is an indispensable tool in demand response (DR) strategies [7]. However, the execution of reliable energy load forecasting is not easy, and several challenges arise in the process [8]. For this reason, researchers focus on overcoming these obstacles using new technologies, such as big data [9]. When energy load forecasting was still nascent, simple methods, such as linear regression [10], hybrid regressions [11], Kalman filters [12], Kalman estimators [13], or autoregressive integrating moving average (ARIMA) [14] and metabolic nonlinear grey models [15], were used. While these models are effective when dealing with linear data, they are unable to provide accurate forecasting in complex, non-linear energy load time series. Load forecasting methods have changed in response to advances in artificial intelligence neural network development [16]. [PERSON] et al. used a neural networks approach for very short energy forecasting [17] and [PERSON] et al. integrated a feature selection to the neural network algorithm [18]. As these models used optimal parameters [19], hybrid methods--basically, artificial neural network optimized methods--were proposed [20]. Many of the optimization methods used rely on feature selection [21] or hybrid feature selection to improve the parameters used for forecasting methodology [22]. Recent research has shown that performing a feature selection when starting to train the algorithm yields better results, as the model will be more likely to learn the characteristics of the time series when dealing with the optimum input-output set [23]. Hybrid algorithms that combine at least two prediction methods when developing the forecasting model have been developed [24]. [PERSON] et al. proposed a support vector regression method enforced with feature selection of data [25]. [PERSON] also proposed a hybrid methodology but using deep learning algorithms [26]. Due to the proven efficiency of these methods, the research presented herein is also based on a hybrid approach.