We propose an online multivariate distributional forecasting model in which we condition the parameters of a vine copula on covariates. An online algorithm updates the parameters sequentially as new observations become available. Existing approaches require full batch re-estimation using all available data at each update step, which makes them computationally prohibitive in large-scale forecasting applications and less suitable for settings in which dependence structures evolve over time. Simulation results show that the online procedure achieves forecasting accuracy comparable to that of the batch estimator, while drastically reducing computation time. We illustrate the method in a forecasting application to electricity net-demand across five regions of Great Britain and show that (i) the conditional vine copula model outperforms an unconditional Gaussian (and vine copula) benchmark and (ii) that online estimation improves forecast accuracy when batch re-estimation is not available. The algorithm is implemented in the Python package ondil.

We propose self-normalized inference methods for time-series expected-shortfall regressions and, as a corollary, for quantile regressions. The procedures avoid bootstrap methods and direct long-run variance estimation, require only expanding-window regression estimates, and remain correctly sized under strong serial dependence. Simulations illustrate their finite-sample performance, while applications to stock-return predictability and Growth-at-Risk demonstrate their practical usefulness.