Abstract

This study proposes and evaluates several hybrid VAR–Neural Network models for multivariate time series forecasting, including VARNN, VAR+Residual-FFNN, and VAR+Residual-LSTM. The main contribution of this research is the application of residual learning, where Neural Networks are trained to learn the residual errors generated by the VAR model in order to improve forecasting accuracy. Experimental results demonstrate that hybrid forecasting models significantly outperform single forecasting models. In particular, VAR+ResidualLSTM and VAR+Residual-FFNN achieved lower forecasting errors compared to direct hybrid approaches such as VAR+FFNN and VAR+LSTM. The findings confirm that residual learning enables Neural Networks to focus on learning nonlinear residual components after VAR captures linear dependencies.

Keywords: Multivariate Time Series, VAR, LSTM, FFNN, Residual Learning, Hybrid Forecasting.