Assessment of Conditional Dependence Structures in Commodity Futures Markets Using Copula-GARCH Models and Fuzzy Clustering Methods

Abstract

The dynamic development of commodity derivatives markets has been observed since the mid-2000s. It is related to the development of e-commerce, the inflow of financial investors’ capital, and the emergence of exchange-traded funds and passively managed index funds focused on commodities. These advances are accompanied by changes in dependence structure in the markets. The main purpose of this study is to assess the conditional dependence structure in various commodity futures markets (energy, metals, grains and oilseeds, soft commodities, agricultural commodities) in the period from the beginning of 2000 to the end of 2018. The specific purpose is to identify the states of the market corresponding to typical patterns of the conditional dependency structure, and to determine the time of transition from one state to another. The copula-based Multivariate Generalized Autoregressive Conditional Heteroskedasticity models were used to describe the dynamics of dependencies between the rates of return on prices of commodity futures, while the dynamic Kendall’s tau correlation coefficients were applied to measure the strength of dependencies. The daily changes in the conditional dependence structure in the markets (changes in states of the markets) were identified with the fuzzy c-means clustering method. In 2000–2018, the conditional dependence structure in commodity futures markets was not stable, as evidenced by the different states of markets identified (two states in the grains and oilseeds market, the agricultural market, the soft commodities market and the metals market, and three states in the energy market).