Modeling Time Series Global Mean Temperature Index Using SARIMA, NARNN, and SARIMA-NARNN Hybrid Models

This study aimed to demonstrate the efficacy of time series models in both modeling and forecasting processes, leveraging extensive monthly global mean temperature index data spanning from January 1880 to December 2016. Employing the Box–Jenkins methodology, this study identified the SARIMA (2,1,2)(0,0,2)12 model with drift as the most suitable fit for the time series, determined by its lowest AIC value. Utilizing the LM algorithm, the empirical results revealed that the NARNN model, comprising 11 neurons in the hidden layer and 6-time delays, exhibited superior performance among nonlinear autoregressive neural network models, boasting a smaller MSE value. While SARIMA and NARNN models excel in addressing linear and nonlinear challenges within time series data, respectively, this study proposes the use of a SARIMA-NARNN hybrid model. By combining SARIMA and NARNN capabilities, this hybrid approach offers a comprehensive solution, effectively addressing both linear and nonlinear modeling requirements. Comparative analyses underscored the superiority of the hybrid model over standalone SARIMA(2,1,2)(0,0,2)12 with drift model and the NARNN model with 11 neurons in the hidden layer and 6 time delays, showcasing higher accuracy through its lowest MSE in this study. These findings contribute significantly to bridging critical gaps in time series forecasting methodologies by leveraging the strengths of both statistical and machine learning approaches.