Wavelet Transforms and Time-Frequency Analysis of Commodity Price Behavior

Russell Davidson and Jean-Baptiste Lesourd
GREQAM-CNRS, University of Aix-Marseille
russell@ehess.cnrs-mrs.fr

Walter C. Labys
West Virginia University
WLabys@wvnvm.wvnet.edu

Abstract

The purpose of this study is to investigate potential empirical applications of wavelet analysis in the context of commodity price behavior. The analysis of the underlying generating processes of commodity price behavior has been of strategic importance to the understanding, forecasting and stabilizing of primary commodity markets. The methods of analyzing this behavior have been based mostly on the time series domain and to a lesser extent on the frequency domain. More recent studies of this nature have concentrated on evaluating prices in the short run in contrast to the medium or long run. Examples of the former include chaotic and fractal estimation which discloses underlying nonlinear dependence. Examples of the latter relate more to the structural time series modeling of medium and long run cyclical components of a stochastic nature. However, such studies have not investigated wavelet transforms as means of combining both the time and frequency interpretations of commodity price behavior.

This study hopes to overcome this problem by utilizing a recently developed wavelet estimation algorithm to analyze the time-frequency behavior of the prices of some 21 primary commodities traded on internationally important markets as well as the aggregated UNCTAD commodity price index. This study begins with a brief review of the basis characteristics of commodity price behavior. Some explanations are also provided of the econometric approaches employed to analyze this behavior. A brief review of the theory of wavelets is then presented followed by definitions of the wavelet estimation algorithm employed and related statistical tests. The empirical results of the estimation process are then examined, including detrending and residual analysis. Finally, conclusions are offered regarding the implications of the findings for explaining commodity price behavior.

In terms of the feasibility of the above study plan, it appears that we have to decide more precisely as to what we want to include in the study. There would seem to be two possible papers based on commodity price analysis: (1) Price behavior is interpreted only in terms of the wavelet tile of patio diagrams; and (2) this price explanation is extended to include the wavelet regression and its residuals, possibly even with implications for price forecasting.