Volatility, Tail Risk and Scaling Diagnostics in Coffee, Brent Oil and Gold Futures: Evidence from Daily Futures Series

Abstract

This article examines volatility, tail risk, temporal dependence, scaling behavior, and simulation-based uncertainty in daily coffee, Brent oil, and gold futures series. The sample spans 4 January 2016 to 31 December 2025 for coffee (2515 logarithmic returns) and Brent oil (2581 returns), and 4 January 2016 to 30 December 2025 for gold (2187 returns). The analysis combines historical Value at Risk (VaR) and Expected Shortfall (ES), rolling volatility, dependence diagnostics, common-date robustness, detrended fluctuation analysis (DFA), multifractal diagnostics, and bootstrap-based Monte Carlo scenarios. The vendor-supplied histories were obtained from Investing.com; observable contract-family, symbol, and quotation metadata were cross-checked against official ICE and CME specifications, while the unavailable vendor rollover algorithm is treated explicitly as a measurement limitation. A synchronized sample of 2162 return dates preserves the principal risk ranking: Brent oil remains the most volatile and records the deepest 1% ES, coffee occupies an intermediate position, and gold remains the least dispersed. DFA estimates are H = 0.460 (95% block-bootstrap CI [0.430, 0.537]) for coffee, H = 0.492 [0.380, 0.569] for Brent oil, and H = 0.436 [0.423, 0.539] for gold. Because all intervals include values near 0.5 and shuffled/AAFT-surrogate benchmarks do not support robust persistence, the evidence does not justify a strong long-memory claim. Multifractal-spectrum results show greater width for Brent oil and gold than for coffee, but shuffled-series comparisons require cautious interpretation. The contribution lies in comparing agricultural, energy and precious-metal futures within a common, reproducible and robustness-tested risk-management framework rather than in proposing a new estimator.