Forecasting Commodity Prices: GARCH, Jumps, and Mean Reversion
Fluctuations in the prices of various natural resource products are of concern in both policy and business circles; hence, it is important to develop accurate price forecasts. Structural models provide valuable insights into the causes of price movements, but they are not necessarily the best suited for forecasting given the multiplicity of known and unknown factors that affect supply and demand conditions in these markets. Parsimonious representations of price processes often prove more useful for forecasting purposes. Central questions in such stochastic models often revolve around the time-varying trend, the stochastic convenience yield and volatility, and mean reversion. The authors seek to assess and compare alternative approaches to modelling these effects, focusing on forecast performance. Three econometric specifications are considered that cover the most up-to-date models in the recent literature on commodity prices: (i) random-walk models with autoregressive conditional heteroscedasticity (ARCH) or generalized ARCH (GARCH) effects, and with normal or student-t innovations, (ii) Poisson-based jump-diffusion models with ARCH or GARCH effects, and with normal or student-t innovations, and (iii) meanreverting models that allow for uncertainty in equilibrium price.
The authors' empirical application uses aluminium price series at daily, weekly, and monthly frequencies. The authors use one-step-ahead out-of-sample forecasts, where parameter estimates are repeatedly updated at every step of the procedure. In addition, in models with jumps, where analytical formulae are not readily available for obtaining conditional expected forecast errors, the authors devise a simple simulation-based procedure to approximate these errors. Their results are as follows. The mean-reverting model with stochastic convenience yield outperforms, to a large extent, all other competing models for all forecast horizons, with high-frequency (daily and weekly) data; within the non-mean-reverting GARCH class of processes analyzed for these frequencies, models with jumps or asymmetries fare best, yet the latter remain dominated by the mean-reverting models. With monthly data, the mean-reverting model still fares well in comparison with the random-walk GARCH class; nevertheless, depending on the forecast horizon and evaluation criteria, non-mean-reverting models with GARCH-in-mean effects dominate to some extent, suggesting that expected risk has a non-negligible effect on price behaviour.
Journal of Forecasting (0277-6693)
July 2008. Vol. 27, Iss. 4, pp. 279-91