Does Trading Volume Improve Long‐Term Volatility Forecasts? Evidence from the MF2‐GARCH Framework

ABSTRACT

We augment the long‐term volatility component of the MF2‐GARCH model of Conrad and Engle (2025) with smoothed trading volume, yielding the MF2V‐GARCH. The extension adds a single parameter , preserves covariance stationarity, and nests the MF2‐GARCH as a special case. Estimation on sixteen US assets (the S&P 500 index, nine sector ETFs, and six individual stocks) over January 2000 to March 2026 reveals that is significant for the S&P 500 (), Apple, and financial‐sector assets, but effectively zero for defensive sectors such as consumer staples and healthcare. Out‐of‐sample, the MF2V‐GARCH produces lower QLIKE losses than the MF2‐GARCH at all twelve forecast horizons for the S&P 500. All twelve one‐sided Diebold‐Mariano tests, computed with HAC variance estimates and small‐sample corrections and confirmed by a stationary bootstrap, are significant at the 5% level under both the QLIKE and squared‐error losses, and the relative root mean squared error at the three‐month horizon falls by 23% on the Conrad‐Engle evaluation window. Sub‐period analysis shows that the volume advantage is largest during regime transitions: during COVID‐19, the MF2‐GARCH's eight‐month forecasts are worse than a historical average while the MF2V‐GARCH remains competitive (a descriptive comparison on the episode's small set of valid origins). Across the full cross‐section, the MF2V‐GARCH wins 151 of 192 horizon‐level comparisons (79%) on the outlier‐screened evaluation design of Conrad and Engle (2025); a new sensitivity analysis shows that on unfiltered forecast origins this advantage attenuates to statistical zero without ever significantly reversing. In a horse‐race against alternative daily information‐arrival proxies, volume outperforms Amihud illiquidity out of sample and is the most robust single proxy across horizons, while the Corwin–Schultz high–low spread fits best in‐sample and performs comparably out of sample (marginally better at several monthly horizons); in characteristic‐sorted portfolios of 238 stocks the volume effect is significant in thirteen of fifteen quintiles at the 5% level and strengthens with size.