Learn the measure, estimate the moment: machine-learned drivers in dynamic conditional correlation models

Yongdeng Xu

No E2026/12, Cardiff Economics Working Papers from Cardiff University, Cardiff Business School, Economics Section

Abstract: Realized measures are biased for the moments of returns. We propose a two-step approach to forecasting large correlation matrices: machine-learned forecasts of realized measures enter a dynamic conditional correlation model as drivers, and their weights are estimated by quasi-maximum likelihood on returns. The correlation recursion is run in a matrix-logarithm parametrization, so every forecast is a valid correlation matrix. For Dow Jones stocks, a learned volatility driver and this recursion improve on a dynamic conditional correlation model with realized drivers at horizons of one, five and 22 days. For S&P 500 stocks, the model fits monthly returns better than machine-learned projections of realized correlations, has no invalid forecast in any month, and trades less. The criterion that selects the weight on a realized driver matters as much as the model, and practitioners can obtain valid forecasts calibrated to returns with standard software.

Keywords: DCC-GARCH-X; Realized measures; Covariance forecasting; Forecast evaluation; Positive definiteness; Log-correlation coordinates; Nonlinear shrinkage (search for similar items in EconPapers)
JEL-codes: C32 C53 C58 G11 G17 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2026-09
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