QED Working Paper Number

Based on recent evidence of fractional cointegration in commodity spot and futures markets, we investigate whether a fractionally cointegrated model can provide statistically and/or economically significant forecasts of commodity returns. Specifically, we propose to model and forecast commodity spot and futures prices using a fractionally cointegrated vector autoregressive (FCVAR) model that generalizes the more well-known (non-fractional) CVAR model to allow fractional integration. We derive the best linear predictor for the FCVAR model and perform an out-of-sample forecast comparison with the non-fractional model. In our empirical analysis to daily data on 17 commodity markets, the fractional model is found to be superior in terms of in-sample fit and also out-of-sample forecasting based on statistical metrics of forecast comparison. We analyze the economic significance of the forecasts through a dynamic trading strategy based on a portfolio with weights derived from a mean-variance utility function. Although there is much heterogeneity across commodity markets, this analysis leads to statistically significant and economically meaningful profits in most markets, and shows that profits from both the fractional and non-fractional models are higher on average and statistically more significant than profits derived from a simple moving-average strategy. The analysis also shows that, in spite of the statistical advantage of the fractional model, the fractional and non-fractional models generate very similar profits with only a slight advantage to the fractional model on average.

Ke Xu
Paresh Kumar Narayan
JEL Codes
commodity markets
economic significance
fractional cointegration
futures markets
price discovery
trading rule
vector error correction model
Working Paper