<p>In this study, we propose a novel approach to model the relationship between bivariate time series by introducing a bivariate vector autoregressive model with Ali-Mikhail-Haq(AMH) copula, incorporating non-normal errors. The utilization of the Ali-Mikhail-Haq copula will allow for flexible modeling of the dependence structure between the two time series. This copula framework enables us to model the joint distribution of the errors with greater accuracy. Our approach provides a way to capture the relationships between the two time series, making it more suitable for complex data structures where traditional methods based on normal error assumptions may fall short. The Inference Functions for Margins (IFM) technique is employed to estimate both the model parameters and the dependency structure in our proposed model. To evaluate the accuracy of the proposed model, we conduct an extensive simulation study. The results demonstrate that the suggested model performs robustly across different scenarios, effectively capturing the dependence structure and delivering precise parameter estimates. The AMH copula efficiently models moderate levels of both negative and positive dependence. To enhance forecasting performance, we introduce a hybrid extension in which an artificial neural network(ANN) is applied to the residuals of the copula-based AMH–VAR model. This hybrid approach captures remaining nonlinear patterns not explained by the linear VAR dynamics and the copula-based dependence structure, leading to improved predictive accuracy. Finally, we apply the proposed models to real-world data, further validating its practical applicability.</p>