AI & ML
Vine Copula VAR:From Recursive Margins to Joint Forecast Inference
arXiv stat.TH0 views
arXiv:2610.07589v1 Announce Type: cross Abstract: Joint-event forecasts often combine a dependence estimate based on past forecast errors with newly estimated marginal distributions. When each historical error retains the marginal fit available at its issue date, inference must account for an overlapping sequence of estimation errors. We derive their joint influence with the terminal forecast 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, while terminal slope uncertainty remains. The resulting covariance estimator gives asymptotically valid repeated-sample intervals for fixed one-sided event probabilities at the realized forecast state. In the Gaussian submodel, retaining issued transforms adds a positive semidefinite covariance term relative to refitting margins on the same observations. Monte Carlo simulations show that terminal-margin uncertainty is quantitatively more important than this additional term and that logit intervals improve lower-tail coverage in the designs studied. A real-time forecasting application to U.S. macroeconomic releases shows how marginal estimation contributes to uncertainty in predicted probabilities of joint contractions and identifies limitations of the stationary marginal model.
Source:https://arxiv.org/abs/2610.07589PreviousPoisson empirical Bayes estimation of sums of random variables via minimum-distance methodsNextAsymptotic Analysis of Empirical Risk Minimization on Entry-wise i.i.d. Heavy-Tailed Data
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