Hybrid methodologies have become popular in many fields of research as they allow researchers to explore various methods, understand their strengths and weaknesses and combine them into new frameworks. Thus, the combination of different methods into a hybrid methodology allows to overcome the shortcomings of each singular method. This paper presents the methodology for two hybrid methods that can be used for time series forecasting. The first combines singular spectrum analysis with linear recurrent formula (SSA-LRF) and neural networks (NN), while the second combines the SSA-LRF and weighted fuzzy time series (WFTS). Some of the highlights of these proposed methodologies are:•The two hybrid methods proposed here are applicable to load data series and other time series data.•The two hybrid methods handle the deterministic and the nonlinear stochastic pattern in the data.•The two hybrid methods show a significant improvement to the single methods used separately and to other hybrid methods.

This study attempted to combine SSA (Singular Spectrum Analysis) with other methods to improve the performance of forecasting model for time series with a complex pattern. This work discussed two modifications of TLSAR (Two-Level Seasonal Autoregressive) modeling by considering the SSA decomposition results, namely TLSNN (Two-Level Seasonal Neural Network) and TLCSNN (Two-Level Complex Seasonal Neural Network). TLSAR consisted of a linear trend, harmonic, and autoregressive component. In contrast, the two proposed hybrid approaches consisted of flexible trend function, harmonic, and neural networks. Trend and harmonic function were considered as the deterministic part identified based on SSA decomposition. Meanwhile, NN was intended to handle the nonlinearity relationship in the stochastic part. These two SSA-based hybrid models were contemplated to be more flexible than TLSAR and more applicable to the series with an intricate pattern. The experimental studies to the monthly accidental deaths in USA and daily electricity load Jawa-Bali showed that the proposed SSA-based hybrid model reduced RMSE for the testing data from that obtained by TLSAR model up to 95%.

Short-term electricity load demand forecast is a vital requirements for power systems. This research considers the combination of exponential smoothing for double seasonal patterns and neural network model. The linear version of Holt-Winter method is extended to accommodate a second seasonal component. In this work, the Fourier with time varying coefficient is presented as a means of seasonal extraction. The methodological contribution of this paper is to demonstrate how these methods can be adapted to model the time series data with multiple seasonal pattern, correlated non stationary error and nonlinearity components together. The proposed hybrid model is started by implementing exponential smoothing state space model to obtain the level, trend, seasonal and irregular components and then use them as inputs of neural network. Forecasts of future values are then can be obtained by using the hybrid model. The forecast performance was characterized by root mean square error and mean absolute percentage error. The proposed hybrid model is applied to two real load series that are energy consumption in Bawen substation and in Java-Bali area. Comparing with other existing models, results show that the proposed hybrid model generate the most accurate forecast

Electricity load forecasting is crucial for effective energy management, particularly in minimizing energy production and distribution costs. Traditional models like SARIMA and Singular Spectrum Analysis (SSA) have been widely used but often need to capture complex nonlinear patterns and deal with data uncertainties. This study aims to develop and evaluate a hybrid forecasting model that combines the Prophet model with a Neural Network Autoregressive (Prophet-NAR) model, referred to as PropNAR. The objective is to enhance the accuracy of hourly electricity load forecasting in Malaysia by addressing the limitations of existing models. The proposed PropNAR integrated the strengths of the Prophet model in capturing deterministic structures, such as trends, seasonality, and holiday effects with the NAR model’s ability to handle nonlinear stochastic relationships. Additionally, SSA-based bagging is employed to manage data uncertainties, and ensemble techniques are applied to further refine the forecasting accuracy. The hybrid PropNAR model demonstrated significant improvements in forecasting accuracy. Specifically, it reduced Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) by approximately 21%-86% compared to the standalone Prophet model. On the Malaysian electricity load datasets, the PropNAR model achieved MAE values ranging from 527.26 to 1023.78, RMSE values from 752.70 to 1498.54, and MAPE values from 1.12% to 2.04%. These results indicate a substantial enhancement over SARIMA and SSA-NAR in handling outliers and data variability. The proposed hybrid PropNAR model offers a robust solution for Malaysian short-term electricity load forecasting, outperforming conventional models in accuracy and reliability.