A fractionally cointegrated VAR analysis of price discovery in commodity futures markets

In this paper we apply the recently developed fractionally cointegrated vector autoregressive (FCVAR) model to analyze price discovery in the spot and futures markets for five non-ferrous metals (aluminium, copper, lead, nickel, and zinc). The FCVAR model allows for long memory (fractional integration) in the equilibrium errors, and, following Figuerola-Ferretti and Gonzalo (2010), we allow for the existence of long-run backwardation or contango in the equilibrium as well, i.e. a non-unit cointegration coefficient. Price discovery can be analyzed in the FCVAR model by a relatively straightforward examination of the adjustment coefficients. In our empirical analysis we use the data from Figuerola-Ferretti and Gonzalo (2010), who conduct a similar analysis using the usual (non-fractional) CVAR model. Our first finding is that, for all markets except copper, the fractional integration parameter is highly significant, showing that the usual, non-fractional model is not appropriate. Next, when allowing for fractional integration in the long-run equilibrium relations, fewer lags are needed in the autoregressive formulation, further stressing the usefulness of the fractional model. Compared to the results from the non-fractional model, we find slightly more evidence of price discovery in the spot market. Specifically, using standard likelihood ratio tests, we do not reject the hypothesis that price discovery takes place exclusively in the spot (futures) market for copper, lead, and zinc (aluminium and nickel).