Using Bayesian Ridge Regression model and ESN for Climatic Time Series Forecasting

Abstract

The analysis of climatic time series variables, especially evaporation forecasts influenced by diverse climate components, is essential for mitigating the hazards associated with climate change and its effects on environmental phenomena, subsequently affecting human and plant health. The weather patterns and temporal conditions will be evaluated during a restricted time frame. Numerous climate variables, including temperature and humidity, demonstrate strong connections, resulting in multicollinearity that undermines the efficacy of conventional linear models and induces instability and considerable variability in model parameters. Moreover, climatic data frequently display erratic variations owing to their dependence on several sources, including sensors and satellites. This results in a nonlinear pattern, leading to considerable geographical and temporal fluctuation, hence complicating modelling efforts with conventional methods. Therefore, there is a necessity for statistical models that can address these issues and systematically manage residuals and uncertainties, which adversely affect the precision of time series forecasting. This study utilized the Bayesian Ridge Regression (BRR) model. This Bayesian adaptation of conventional ridge regression considers model parameters as random variables instead of constants, thereby diminishing estimate bias and enhancing stability in the presence of multicollinearity. The model offers a probabilistic representation of outputs, facilitating confidence intervals for forecasting and improving the reliability of results. Moreover, climatic time series forecasting is influenced by their chaotic and nonlinear characteristics. This is the point at which the echo state network (ESN) is relevant. This specific sort of recurrent neural network excels at forecasting nonlinear time series due to its proficiency in managing temporal dynamics and nonlinear modelling. This study integrated and hybridized the BRR model within the ESN architecture to utilize its overfitting mitigation capabilities and structural attributes for enhanced forecast accuracy. Experimental findings indicated that the BRR-ESN hybrid model markedly surpassed traditional models in multivariate time series forecasting, validating its efficacy in addressing the structural and climatic intricacies of evaporation data and the associated climate variables.