Have aluminium and copper futures markets become more volatile over time?
Within the industrial metals industry, there has been a great deal of interest surrounding trends in volatility over time. This paper uses a rolling AR(1)-GARCH(1,1) model to estimate and forecast the volatility processes for daily returns on the futures prices of two important non-ferrous metals, aluminium and copper.
The LME is the major international market for the main industrially-used non-ferrous metals, namely aluminium, aluminium alloy, copper, lead, nickel, tin, and zinc. Aluminium has the highest volume of spot and futures trade on the exchange, followed closely by copper. The two metals are also amongst the most important metals in an industrial sense.
Changes in the prices of aluminium and copper are often closely aligned with changes in global industrial production, but also reflect market specific events, compliment and substitute relationships between the physical metals in production, and financial market type influences. Brunetti and Gilbert [1995] characterise two sources of volatility in non-ferrous metals markets, those related to financial market considerations and those related to market fundamentals. Financial considerations include information effects, speculative pressures and hedging activity, usually giving rise to short-run volatility effects. Market fundamentals refer to the underlying availability, supply and demand of physical metal. Fundamentals are a source of long term volatility in metals markets, primarily due to the lags involved in demand and supply side changes.
In this paper, the rolling model is used to examine how the processes driving aluminium and copper returns volatility have evolved over a long sample. Settlement price data on 3-month futures contracts traded on the London Metals Exchange (LME) is used to calculate the daily returns series. The sample consists of daily data for 3-month futures settlement prices in US dollars for aluminium over the period 1 October 1982 to 15 July 2005, and for copper over the period 5 January 1976 to 15 July 2005. The model is estimated using a rolling window of 1000 observations, which iterates 4671 times for aluminium, and 6448 times for copper.
The models are used to examine when and in what manner the α and β coefficients, as estimated parameters of the volatility process, change over time. Estimates are presented graphically. The α estimates for both metals indicate that short-run persistence varies in magnitude through each sample. Similarly, the β estimates also vary markedly over time. The long run persistence of volatility, α+β, is also non-constant over the sample. Moment conditions, specifically the second and fourth, are examined in order to evaluate the statistical properties of the empirical models. One-step-ahead forecasts are also generated and compared with a measure of the ‘true’ volatility, as defined by Pagan and Schwert [1990]. Several forecast evaluation criteria are also applied to the series of forecasts.
The results of the paper suggest that, while the volatility of returns does not appear to display an upward trend, relative to the 1980’s there are periods over the following years where the process driving time-varying conditional volatility appears to have become more variable, and to some degree harder to model at some times using a simple GARCH specification. The variation over time seen in the volatility process as modelled by GARCH suggests that, while volatility in returns has not necessarily increased, volatility in metals markets is itself volatile when analysed over a long horizon. Of course, instability in the GARCH model may indicate that a more complex volatility model is required to better reflect the volatility process in the data.
Keywords: - Volatility forecasting, GARCH, Rolling models, Futures contract, Industrial metals