Alternative GARCH Specifications and Autoencoder-Based Shrinkage for the DCC-NL Covariance Framework

Engle et al. (2019) marry two previously separate strands of the literature—time-series GARCH dynamics and cross-sectional nonlinear shrinkage—into the DCC-NL framework for large dynamic covariance matrices. We extend this marriage along two orthogonal dimen- sions, one for each step of the DCC-NL pipeline: (i) replacing the standard GARCH(1,1) in Step 1 with asymmetric GARCH variants—EGARCH(1,1,1), which captures the lever- age effect, and GARCH(2,1)-DCC-NL, which allows richer short-term dynamics—building on the direction suggested by De Nard et al. (2022, Remark 2.1); (ii) replacing the an- alytical QuESTimate shrinkage in Step 2 with a learned eigenvalue autoencoder trained via a two-phase curriculum of unsupervised denoising and QuESTimate-supervised distil- lation. Both modifications are independent and can be combined. Using the same CRSP data and portfolio-construction rules as De Nard et al. (2022) (with two minor implementa- tion deviations documented in Section 6), we evaluate all models on unconstrained Global Minimum Variance (GMV) portfolios across universe sizes N ∈{100,500,1,000}, and on Markowitz-momentum portfolios at N=1,000, over the period 12/18/1998–12/31/2018. At N=1,000, the eigenvalue autoencoder achieves the lowest annualised portfolio standard de- viation (6.99% vs. 7.37% for DCC-NL) and the highest net-of-cost information ratio (0.75 vs. 0.70), while maintaining the lowest turnover and maximum drawdown. EGARCH de- livers the highest gross Sharpe ratio (0.87 in GMV, 1.01 with momentum) at the cost of substantially higher turnover; net of transaction costs it is dominated by the standalone au- toencoder. The autoencoder Pareto-dominates DCC-NL on all practical metrics: lower SD, higher net IR, lower turnover, and lower maximum drawdown. The combined EGARCH- DCC-AE model matches the standalone autoencoder’s risk metrics. The improvements are concentrated at N = 1,000, where the high concentration ratio (c = N/T ≈0.8) makes covariance estimation most challenging; at smaller universe sizes the gains are marginal.