Higher Order Dynamic Network Linear Models for Covariance Forecasting

Abstract

We forecast the realized covariance matrix of a subset of S&P 500 stocks using GNAR, a class of linear auto-regressive network models. By treating the stocks as nodes in a graph, we use the variance-correlation (DRD) decomposition to construct separate networks for correlations and volatilities. We exploit sparsity in the correlation adjacency matrix to capture higher-order neighbourhood interactions, and build a time-varying Graphical Lasso volatility network using daily log returns. This is, to our knowledge, the first attempt to incorporate a time-varying graph structure in forecasting covariance matrices. Our approach reduces out-of-sample forecasting errors during volatile trading days and improves the Sharpe ratio while reducing turnover in a Long-Only Minimum Variance portfolio compared to previous benchmarks. While sensitive to model update frequency, and non-linear interactions between correlations and volatilities obscure the performance drivers, it shows similar benefits when applied to a broader stock universe.

Keywords: Covariance forecasting, Network linear models, High-frequency time-series, Graph analysis

JEL Classification: C33, C53, C55