Related commodity markets and conditional correlations

Related commodity markets have two characteristics: (i) they may be expected to follow similar volatility processes; (ii) such markets are frequently represented by a market aggregate or index. Indices are used to represent the performance and aggregate time series properties of a group of markets. An important issue regarding the time series properties of an index is how the index reflects the corresponding properties of its components, particularly with regard to volatility and risk. This paper investigates the volatility of a market index relative to the volatility of its underlying assets by analysing correlation matrices derived from rolling AR(1)-generalised autoregressive conditional heteroskedasticity (GARCH)(1,1) model estimates. The second moment properties of a linear aggregate of ARMA processes with GARCH errors are analysed and compared with the properties of the individual returns series. Empirical application is made to the markets for non-ferrous metals on the London Metal Exchange (LME). The volatility of the LME Base Metals Index (LMEX) is modelled and compared with the volatility of the 3-month futures contracts for aluminium, copper, lead, nickel, tin, and zinc.