Forecasting copper prices in the short and medium terms using geostatistics

Abstract The copper price traded in the London Metal Exchange is a key factor for mining companies and for defining macroeconomic policies of producing countries like Chile. In this paper, the authors first review several methods currently used to forecast commodity prices, based on econometrics or statistics, in particular, time series analysis. The authors then propose an alternative methodology centred on geostatistical techniques such as co-kriging, lognormal kriging, and conditional simulations. This methodology is of interest in other application fields that are concerned with forecasting, for instance, discounted cash flow analysis and option pricing theory.
Statistical and geostatistical methods are compared through an exercise based on ex-ante forecasts of the annual copper price within the period 1975-2000, that is, the fitting of the model parameters and the copper price extrapolations only rely on earlier information than the first forecasted year. The forecasts are performed in the short and medium terms, from one to five years ahead. Three analyses are realized: the first one uses the annual copper prices as input information, the second one, the monthly copper prices, whereas the last one includes the monthly information of several auxiliary variables related to the copper market, substitute markets, and world economic indices (these are the copper stock and the nominal US dollar price expressed in 2000 Chilean pesos). Finally, the quality of the forecasts are compared on the basis of several statistical criteria, in particular, the average error, mean absolute, and quadratic errors.
Such comparison leads to the following conclusions. First, the use of monthly information instead of annual information improves all ofthe quality criteria. Second, the multivariate information is not so relevant for improving the forecasts because no auxiliary variable anticipates the copper prices (all of the time series have a synchronous evolution), hence the additional information is redundant with the copper prices. Third, the geostatistical estimators generally behave better than the tested statistical methods (random walk and autoregressive model of first order). Fourth, the information brought by the monthly and multivariate series hardly improves the medium-term forecasts, that is, the extrapolation becomes more imprecise when the number of years increases. Finally, no estimator prevails over the others for all the quality criteria. In this respect, conditional simulations constitute a more interesting tool than kriging, since they allow computing several estimates for the future copper prices, for instance, the mean or the quartiles of the set of realizations.
Another advantage of geostatistics over traditional methods is the ability to assess the uncertainty associated with the unknown future prices. Such assessment has a crucial importance in decision-making, from both a macroeconomic and a microeconomic point of view. The uncertainty is measured through estimation variances or confidence intervals, depending on the technique used (kriging or simulations). Once applied to the ex-ante forecast exercise, the kriging variances turn out to be quite representative of the actual error dispersions. In contrast, the confidence intervals are validated satisfactorily only for the one-year forecast. This is a critical aspect when resorting to simulations for extrapolation purposes: the stochastic model relies on a stationarity assumption and does not account for structural changes in the price behaviour such as trends, therefore only the short-term uncertainty is well assessed.
Keywords: Time series analysis, Kriging, Conditional simulations, Multivariate geostatistics
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