A double mixture autoregressive model of commodity prices

Abstract

Abstract Many commodity prices exhibit boom-bust type behavior: sustained periods of price increases, followed by sudden sharp collapses. Since around the year 2000, booms have become longer while busts have tended to be short but steep, suggesting a structural change in growth and persistence. We model these features of the data using a novel double mixture autoregression with two independent hidden Markov chains. One chain tracks shifts in mean growth rates that account for rising and falling prices, while a second chain tracks changes in volatility and lag-structure. While the two chains are independent, the persistence of price growth depends on the volatility state, which allows the lag-structure to vary across variance regimes. Estimation requires a two-stage Fisherian approach. Initially, location-related parameters are estimated while suppressing the underlying autoregressive structure. These parameters are then held fixed while the optimal lag-structure across variance regimes is determined. We apply the model to three industrial commodities price time series: Crude Oil, Aluminum, and Rubber. We find that in each case, the model captures boom and bust cycles, with data from more recent periods exhibiting higher volatility, longer price rallies, and steeper collapses.