Introduction Testing for Stationarity Testing for Normality Testing for Independence Testing for Linear or Nonlinear Dependence Linear Model Specification Nonlinear Model Specification Testing for Model Order Testing for Residual Process Computational Methods for Performing the Tests
Traditionally, commodity prices have been analyzed and modeled in the context of linear generating processes. The purpose of this dissertation is to address the adequacy of this work through examination of the critical assumption of independence in the residual process of linearly specified models. As an alternative, a test procedure is developed and utilized to demonstrate the appropriateness of applying generalized conditional heteroscedastic time series models (GARCH) to agricultural commodity prices. In addition, a distinction is made between testing for independence and testing for chaos in commodity prices. The price series of interest derive from the major international agricultural commodity markets, sampled monthly over the period 1960--1994. The results of the present analysis suggest that for bananas, beef, coffee, soybeans, wool and wheat seasonally adjusted growth rates, ARCH-GARCH models account for some of the non-linear dependence in these commodity price series. As an alternative to the ARCH-GARCH models, several neural network models were estimated and in some cases outperformed the ARCH family of models in terms of forecast ability. This further demonstrated the nonlinearity present in these time series. Although, further examination is needed, all prices were found to be non-linearly dependent. It was determined by use of different statistical measures for testing for deterministic chaos that wheat prices may be an example of such behavior. Therefore, their may be something to be gained in terms of short-run forecast accuracy by using semi-parametric modeling approaches as applied to wheat prices.
Commodity price behavior holds much interest not only because these markets are affected by waves of speculative activity similar to security markets but more so that these commodities are linked to industries which purchase them and developing country producers which supply them. Commodity spot and future prices have thus been studied extensively. This research extends this work by employing recent fractal approaches to evaluate how the apparent random movements associated with short term behavior can also persist when examining long run behavior. We thus test for the presence of a persistent and finite variance component (i.e. long memory stationary process) as opposed to an infinite variance component (i.e. short memory nonstationary process) in a selected group of international commodity price series. Both fractal and persistent dependence hypotheses and test statistics have been employed. Estimates made of the power law exponent and of the nonintegral or fractional exponent suggest generating processes which are closer to black noise than to white, pink or brown noise.
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