Using Bayesian AR-ESN for climatic time series forecasting - Hasan, Shahla Tahseen; Shukur, Osamah Basheer (Statistics, Optimization & Information Computing, 2025)
Bayesian ARIMA models will offer a solid approach for analyzing time series data, providing more flexibility than traditional recursive models. They also effectively combine previous knowledge with current data to handle uncertainty. A particular kind of Bayesian ARIMA model with comparable considerations is called a Bayesian AR model. While Bayesian models employ prior information to estimate a wide range of possible parameter values, older methods frequently use maximum likelihood estimation to obtain single values for parameters. In order to effectively handle uncertainty, they also develop a posterior distribution. The applicability of Bayesian techniques to AR(p) models is examined in this work. It demonstrates their capacity to manage noisy, non-stationary, or incomplete data while allowing for thorough probabilistic inference, which improves uncertainty comprehension and validates probabilistic forecasts. The Bayesian AR model states that present values are linearly dependent on past values, which are further amplified by white noise. We use previous distributions to evaluate the variance and establish the model parameters. Consequently, these values are adjusted in response to observations, resulting in more complex and adaptable dimensional distributions. The Bayesian ARIMA model aids in forecasting and drawing conclusions when time series are more complicated and need variance considerations. Bayesian AR(p) models display the temporal correlations between data points regardless of how stationary they are. These models are commonly estimated using Markov Monte Carlo (MCMC) techniques like Metropolis-Hastings and Gibbs sampling. These models perform well when handling asymmetry, incomplete data, and structural changes. Even when used in a Bayesian manner, traditional models struggle to capture uncertain time series or intricate nonlinear patterns. These contemporary issues can be resolved with the appropriate use of an Echo State Network (ESN). An effective recursive neural network for forecasting evolving time series is the ESN. To identify the most effective inputs for the ESN, the hybrid Bayesian ARESN methodology utilizes the optimal configuration of the Bayesian AR model. The capacity of this approach to accurately simulate nonlinear interactions is recognized. A Bayesian AR model and an ESN model were integrated in this hybrid Bayesian AR-ESN methodology study. The results show that combining Bayesian AR and ESN significantly increases forecasting accuracy, particularly when forecasting error metrics are used. When compared to conventional techniques, the Bayesian model significantly increases predictive accuracy.