Quantifying Short-Duration Data Patterns In Mineral Prices - Introduction

When data points, plotted on X-Y coordinates, lie along a simple line, their regression can be matched to a high degree of accuracy by one or other simple algebraic expression (Boot and Cox, 1970). Under these conditions, interpolation is axiomic. Further, if the expression defines no more than a straight line, a parabola or other such line which can be related to some specific mechanism which generates the points, then extrapolation might be valid. However, any extrapolation would depend on the continued, unchanged functioning of the mechanism. Studies of more intricate assemblages of data points have long been based on representation by means of series (Fourier, 1811). If sufficiently complicated, several different algebraic expressions can represent the same intricate regression accurately (Hoerl, 1954). However, without reference to a mechanism, no extrapolation is contemplated. Typically, variations in the prices of minerals with time are. sufficiently complicated to render invalid any simple attempts at extrapolation. The computer, however, can be used to derive algebraic expressions which match complicated regressions and also can be represented by the functioning of a mechanism (Becker, 1984). The techniques involved have been applied with advantage in the study of time series representations of mineral prices.