Comparing forecasting accuracy of selected grey and time series models based on energy consumption in Brazil and India

The study compares the forecasting performance of the grey type models, represented by an optimized nonlinear grey Bernoulli model (ONGBM), a nonlinear grey Bernoulli model with particle swarm optimization (NGBM-PSO), and a standard GM with a classic time series model, represented by Auto-Regressive Integrated Moving Average (ARIMA). The models are compared based on simulations and energy consumption forecasting in Brazil and India at aggregate and disaggregate levels from 1992 to 2019. The study illustrates the picture of the Brazil and India energy consumption nexus at aggregate and disaggregated levels. The forecasting accuracy is compared using standard measures such as MAPE, MSE, RMSE, and normalized RMSE. The Diebold-Mariano test findings validates the ARIMA (1,1,1), GM (1,1), ONGBM (1,1) and NGBM (1,1)-PSO models' equal predictive performance. The models are used to compute forecast combinations, ensuring smaller forecasting errors than single models. Optimizing NGBM (1,1) using two algorithms ensures the highest forecasting efficiency for short time series. The results allow a recommendation to use ONGBM (1,1) and NGBM (1,1)-PSO models in the short-term forecasting of energy consumption and combine these forecasts with forecasts from GM (1,1) and ARIMA (1,1,1) models in practical applications.