| A fractal structure is a set of systematic rules that governs movements of an object or phenomenon through time and space. It is self-similar in that smaller pieces of an object are related to the whole, and it has fractional dimension. Natural fractals are called random fractals and they are governed by the combinations of generating rules randomly chosen at different scales. Many economic time series can be treated as random fractals. They may have fractal structures over a range of time scales, and the formation is governed by complex nonlinear dynamic processes. If a time series has fractal structure, the series will manifest fractional Brownian motion and/or the stable distribution.; This study aims to detect fractal structures in the time series of major agricultural commodity cash prices in the U.S. The RJS analyses and stable distribution models are used to analyze fractional Brownian motion and the stable distribution and to characterize non-normal leptokurtosis, long-term memory, self-similarity, and fractional dimension of the series. A reason for the existence of fractals in the price series is discussed, using the fractal market hypothesis and a demand-supply system.; The empirical results indicate evidence of long-term memory for the series; the series do not follow a randomwalk, and the Gaussian assumption is not appropriate. The series have long-term persistent memory with abrupt large changes, fractional dimension, and self-similarity. These properties indicate that the series can be described accurately by fractals.; The empirical results have important implications in market analyses. First, in the presence of fractals, the efficient market hypothesis is no longer appropriate, and thus alternatives such as the fractal market hypothesis are needed. Second, with information on other frequencies in a time series we can predict the behavior of a frequency of the series, using self-similarity. Third, if one considers long-term memory, better forecasting power will be gained; one can increase the credibility of forecasting by considering both short-term and long-term dependence simultaneously. Fourth, it is revealed that the series follow the black noise process, comprising long-term persistent memory with abrupt large changes over markets' various trading horizons. This implies that risk management of market participants can be improved using information on the black noise process. Fifth, the value of the information is illustrated using a hedging demand model. Since the stable distribution describes extreme events effectively, the distributional information provides benefits to hedgers. Sixth, the implications of undefined or infinite mean and variance in economic analyses are discussed in the context of fractal economic time series. |
