Review of Quantitative Finance and Accounting, 20: 245–265, 2003
2003 Kluwer Academic Publishers. Manufactured in The Netherlands.
Forecasting Changes in Copper Futures Volatility
with GARCH Models Using an Iterated Algorithm
KENNETH L. SMITH
Visiting Professor of Finance, Department of Finance, Insurance, and Real Estate, Fogelman College of Business
and Economics, The University of Memphis, Memphis, TN 38152
Associate Professor of Finance, Department of Economics, Finance, & Banking, Kelce College of Business,
Pittsburg State University, Pittsburg, KS 66762
Abstract. There is a gap in the literature regarding the out-of-sample forecasting ability of GARCH-type models
applied to derivatives. A practitioner-oriented method (iterated cumulative sum of squares) is applied to detecting
breakpoints in the variance of two copper futures series. Short-, intermediate-, and long-term out-of-sample
forecasts of copper future series are compared to forecasts from a benchmark random walk model for each series.
Not only do the GARCH-type models dominate the random walk model, but the relative improvement is fairly
consistent across series, forecast horizon, and GARCH-type model. The evidence makes clear that, with few
exceptions, the forecast improvement of the GARCH-type models over the RW model lies somewhere between
20–30%. It is particularly true that for the long-term close to close forecasts, there is great coherence among the
forecasts. These all fall within a fairly narrow range.
Key words: futures, GARCH, volatility
JEL Classiﬁcation: G0, G1
Estimation of parameters of any model requires a certain amount of stability in the underly-
ing structure. That is, a stable mean and variance are required to perform any procedure that
seeks the proper speciﬁcation. It is well known that ﬁnancial time series are highly volatile.
This has been documented for both equity and futures markets. This volatility ensures that
out-of-sample forecasting is imprecise (see Figlewski, 1997). If the underlying data gener-
ating process cannot be known with certainty, any assumption about extending parameter
stability for the in-sample period to the out-of-sample forecast period may be questionable.
Much research effort has been expended on modeling ﬁnancial variables. Modeling is of
little value unless the model is able to reasonably predict the future path of the variable in
question. It may be difﬁcult to argue that a forecaster can accurately predict any ﬁnancial
variable for more than a few days ahead. However, there is usually some degree of stability