Abstract:
This paper develops a High-Dimensional Distributional Vector Autoregression (HiDVAR), a real-time, data-rich framework for forecasting the joint predictive distribution of GDP growth, inflation, and unemployment without imposing a parametric density shape. The motivation is policy risk monitoring: standard quantile-to-density pipelines can compress one-sided inflation risks in turbulent periods, especially when they rely on restrictive distributional modeling or forecast anchors. HiDVAR combines distribution regression (many binary threshold models), local projections, elastic-net shrinkage, and factor-based information extraction from an augmented real-time FRED-QD panel, and then constructs coherent multivariate, path-consistent scenarios using a triangular factorization and copula-based simulation. In real-time out-of-sample evaluation (February 2013-June 2025), HiDVAR improves probabilistic forecast accuracy relative to the FRBNY Outlook-at-Risk framework and standard benchmarks, with the largest gains concentrated in inflation tail-risk assessment. Relative to the FRBNY model, HiDVAR reduces CPI inflation CRPS by 28% and the multivariate Energy Score by 22%, with a weakly significant Energy Score improvement in Diebold-Mariano tests. During the post-pandemic inflation surge, HiDVAR assigns substantially more probability mass to persistent high-inflation outcomes and produces earlier, better-calibrated upper-tail risk signals. A policy application maps the predictive distributions into risk-scenario probabilities and rule-implied policy-rate distributions, illustrating the value of flexible density forecasting for macro risk monitoring.
