This study aims to investigate the relationship between the spot and futures commodity markets. Considering the complexity of the relationship, we use a nonlinear autoregressive distributed lag (NARDL) framework that considers the asymmetry and nonlinearity in both the long and short run. Based on the daily returns of six commodity indices reaggregated on three commodity types, our study reaches some interesting findings. Our analysis highlights a bidirectional relationship between both markets over the short and long run, with a greater lead for the futures market. This result confirms the future market's dominant contribution to price discovery in commodities. Changes in commodity prices appear first in the futures market, as informed investors and speculators prefer trading on this market that is characterized by low costs and a high-leverage effect. Then, the information is transmitted from the futures to the spot market through arbitrageurs' activity, which explains the nonlinearity of the relationship. These results are helpful to scholars, investors and policymakers.

中文翻译：

---

重新审视现货和期货市场之间的关系：来自商品市场和 NARDL 框架的证据。

本研究旨在调查现货和期货商品市场之间的关系。考虑到关系的复杂性，我们使用非线性自回归分布滞后 (NARDL) 框架，该框架考虑了长期和短期的不对称性和非线性。根据重新汇总在三种商品类型上的六种商品指数的每日收益，我们的研究得出了一些有趣的发现。我们的分析强调了短期和长期两个市场之间的双向关系，期货市场的领先优势更大。这一结果证实了未来市场对商品价格发现的主要贡献。商品价格的变化首先出现在期货市场，因为知情的投资者和投机者更喜欢在这个以低成本和高杠杆效应为特征的市场上进行交易。然后，信息通过套利者的活动从期货传递到现货市场，这解释了这种关系的非线性。这些结果对学者、投资者和政策制定者都有帮助。