Topology of intraday realized volatilities across commodity indices, copper futures, the U.S. dollar index, and the NASDAQ: An unrestricted multivariate HAR-VAR approach

This study examines volatility connectedness across five main markets, i.e., agricultural commodities (JJA), energy commodities (JJE), copper futures (HG), the U.S. Dollar Index (DX), and the NASDAQ Composite (CQ). We use high-frequency realized volatility and a horizon-dependent connectedness framework by leveraging the Heterogeneous Autoregressive (HAR) model. We present a novel Unrestricted Multivariate HAR (UMHAR) approach with an extended joint connectedness method to capture volatility spillovers at daily, weekly, and monthly horizons. Our sample is from September 28, 2009, to June 7, 2023, and includes key systemic events, such as the aftermath of the global financial crisis, COVID-19, and the Russo-Ukrainian war. Both static and dynamic network analysis show different horizon-specific spillover patterns. Net volatility transmissions primarily occur on the daily horizon, while at the weekly horizon, they are mostly neutralized. On the monthly horizon, the shocks are gradually absorbed over time. The significance of copper as an “economic barometer" is confirmed by its crucial role within the system. Dynamic analysis reveals major peaks in the overall connectedness during systemic crises, suggesting elevated contagion risks. Agricultural commodities become net transmitters during the Russo-Ukrainian war due to supply chain disruptions. During COVID-19, energy commodities changed from being shock absorbers to transmitters. Copper has a significant impact on the system during the 2010-2011 post-crisis industrial recovery. The influence of the U.S. dollar and NASDAQ depends on monetary policy and technology-sector sentiment cycles. We confirm the robustness of our findings by comparing UMHAR-VAR results with alternative model structures, sub-sample tests, and standard VAR-based indices. These results demonstrate how cross-market spillovers are determined by horizon-dependent volatility dynamics. They offer practical insights to market regulators, macroprudential policymakers, and long-term investors who aim to improve portfolio strategies and lower systemic risk.