A new fuzzy-fractal approach for forecasting financial and economic time series

The authors describe a novel method for estimating the fractal dimension of a geometrical object using fuzzy logic techniques. The fractal dimension is a mathematical concept, which measures the geometrical complexity of an object. The algorithms for estimating the fractal dimension calculate a numerical value using as data a time series for the specific problem. This numerical (crisp) value gives an idea of the complexity of the geometrical object (or time series). However, there is an underlying uncertainty in the estimation of the fractal dimension because we use only a sample of points of the object, and also because the numerical algorithms for the fractal dimension are not completely accurate. For this reason, we propose a novel definition of the fractal dimension that incorporates the concept of a fuzzy set. This new fuzzy-fractal approach was applied to the problem of forecasting the prices of two consumer goods in the US, for the 1994-2000 period, with very good results