A Comparative Study of Bayesian Regularization Neural Network and Multilayer Perceptron Neural Network in the Hybridization of Self-Exciting Threshold Autoregressive Models

Abstract

Artificial Neural Networks (ANNs), particularly Bayesian Regularization Neural Networks (BRNNs), have demonstrated strong capabilities for modeling complex nonlinear patterns in time-series data. This study explores the hybridization of Self-Exciting Threshold Autoregressive (SETAR) models with BRNN and Multilayer Perceptron Neural Networks (MLPNNs) to improve forecasting accuracy of nonlinear cyclical data, using the Canadian Lynx dataset. The hybrid models aim to capture regime shifts and nonlinear dynamics more effectively. Results show that the SETAR-BRNN hybrid outperforms individual models and other hybrids, achieving a Mean Absolute Percentage Error (MAPE) of 2.261%, representing a 45.8% reduction compared to the standalone SETAR model (MAPE = 4.17%) and a 14.7% reduction compared to BRNN alone (MAPE = 2.65%). Additionally, the SETAR-BRNN model reduces the Root Mean Square Error (RMSE) by 65.3% relative to the MLPNN-SETAR hybrid and suggest a forecasting performance across multiple horizons. The findings indicate that integrating BRNN into the SETAR framework significantly enhances predictive accuracy and model robustness for nonlinear, regime-dependent time series. This highlights the effectiveness of the SETAR-BRNN hybrid approach in accurately modeling complex cyclical behaviors and regime shifts in real-world data.