Vine Copula VAR:From Recursive Margins to Joint Forecast Inference

Joint-event forecasts combine an estimated dependence model with current marginal forecasts. Retaining historical transforms at the marginal fits available when each outcome arrived creates overlapping estimation errors. We derive their joint influence with the terminal estimates in a stable Vine Copula VAR with normal innovation margins and a fixed, correctly specified Gaussian or positive Clayton vine. An intercept identity and the stable VAR filter reduce the historical correction to harmonically weighted innovation moments. Terminal slope uncertainty remains in the forecast gradient. A feasible covariance estimator yields asymptotically valid repeated-sample intervals for fixed one-sided event probabilities at the realized forecast state. A same-family terminal refit provides the efficiency comparison. Retaining dated transforms adds a positive semidefinite limiting covariance term, whose event-level cost depends on dependence sensitivity and forecast-state leverage. Monte Carlo comparisons show a small accuracy cost of retaining the transforms and a larger inferential role for current marginal estimation. Allowing Clayton dependence improves downside forecasts relative to Gaussian dependence under each transform rule. A fourteen-variable U.S. real-time forecasting application and simulations with twenty and fifty variables illustrate feasible joint-event estimation and analytic inference for fixed-depth vines.