Searching for fractal structure in agricultural futures markets

The four parameters of the Pareto stable probability distribution for six agricultural futures are estimated. The behavior of these estimates for different time-scaled distributions is consistent with the conjecture that the stochastic processes generating these agricultural futures returns are characterized by a fractal structure. In particular, it is empirically verified that the six futures returns satisfy the property of statistical self-similarity. Moreover, the same time series is analyzed by using the so-called rescaled range analysis. This analysis is able to detect both the fractal structure and the presence of long-term dependence within the observations. The Hurst exponent with the use of two methods, the classical and modified rescaled analysis, is estimated and tested. Finally, with the use of Mandelbrot’s result on the existence of a link between the characteristic exponent of a stable distribution and the Hurst exponent, further empirical confirmation is found that the processes generating agricultural futures returns are fractal.

The four parameters of the Pareto stable probability distribution for six agricultural futures are estimated. The behavior of these estimates for different time-scaled distributions is consistent with the conjecture that the stochastic processes generating these agricultural futures returns are characterized by a fractal structure. In particular, it is empirically verified that the six futures returns satisfy the property of statistical self-similarity. Moreover, the same time series are analyzed by using the so-called rescaled range analysis. This analysis is able to detect both the fractal structure and the presence of long-term dependence within the observations. The Hurst exponent with the use of two methods, the classical and modified rescaled analysis, is estimated and tested. Finally, with the use of Mandelbrot’s result on the existence of a link between the characteristic exponent of a stable distribution and the Hurst exponent, further empirical confirmation is found that the processes generating agricultural futures returns are fractal.