The present study investigates the price (co)volatility of four dairy commodities—skim milk powder, whole milk powder, butter, and cheddar cheese—in three major dairy markets. It uses a multivariate factor stochastic volatility model for estimating the time-varying covariance and correlation matrices by imposing a low-dimensional latent dynamic factor structure. The empirical results support four factors representing the European Union and Oceania dairy sectors as well as the milk powder markets. Factor volatilities and marginal posterior volatilities of each dairy commodity increase after the 2006/07 global (food) crisis, which also coincides with the free trade agreements enacted from 2007 onward and EU and US liberalization policy changes. The model-implied correlation matrices show increasing dependence during the second half of 2006, throughout the first half of 2007, as well as during 2008 and 2014, which can be attributed to various regional agricultural dairy policies. Furthermore, in-sample value at risk measures (VaRs and CoVaRs) are provided for each dairy commodity under consideration.

中文翻译：

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关于国际乳制品市场的联合波动动态*

本研究调查了三个主要乳制品市场中四种乳制品（脱脂奶粉、全脂奶粉、黄油和切达干酪）的价格（共）波动性。它使用多变量因子随机波动率模型通过强加低维潜在动态因子结构来估计时变协方差和相关矩阵。实证结果支持代表欧盟和大洋洲乳制品行业以及奶粉市场的四个因素。2006/07 全球（食品）危机后，每种乳制品的因子波动率和边际后验波动率增加，这也与 2007 年以后颁布的自由贸易协定以及欧盟和美国的自由化政策变化相吻合。模型隐含的相关矩阵在 2006 年下半年表现出越来越大的依赖性，整个 2007 年上半年以及 2008 年和 2014 年期间，这可归因于各种区域农业乳品政策。此外，还为所考虑的每种乳制品提供了样本内风险测量值（VaR 和 CoVaR）。