<p>Long-term streamflow probabilistic forecasting is crucial for water resources prediction and scheduling. Traditional methods of long-term streamflow forecasting assume streamflow as stationary series with residual variance modeled as white noise, which violates the dynamic variation characteristics of real-time forecast error. This study employed a method based on the vector autoregression (VAR) model for point forecasting, coupled with an Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH) model and the t-Copula function for long-term streamflow probabilistic forecasting. The VAR model predicts the deterministic streamflow process at multiple sites, while the EGARCH model describes the conditional heteroscedasticity of the VAR model residuals. Subsequently, the higher-order spatial–temporal dependence of multivariate stochastic variables is identified using the t-Copula function. Application of the proposed method to interbasin streamflow predictions for the Xiluodu and Three Gorges reservoirs revealed the following. (1) The variance of streamflow forecast residuals exhibits autocorrelation and is influenced by past residuals. The EGARCH model can capture the asymmetrical impact of positive and negative residual values on the variation, thereby delicately characterizing the heteroscedasticity of the residuals. (2) The t-Copula function can accurately quantify the contemporaneous correlations implicit in the forecast residual variances and capture the nonlinear dynamic dependencies. (3) The interval prediction that introduces the copula function to capture implicit nonlinear characteristics has a lower average interval width and a lower average relative bandwidth value than the interval prediction that only uses the GARCH model to describe the heteroscedasticity of residuals.</p>