Remarks on evaluation of correlation dimension for 5 French stock data

Fractal correlation dimension (D₂) was introduced by Grassberger and Procaccia (1983) when considering some deterministic models originating from differential equations. Since then D₂ was applied in many situations; it has become also a tool in statistical data analysis of data burdened with noise. The presented paper attempts to emphasize the difficulties and uncertainties met when calculating correlation dimension for real time data observed as time series. In such situation the correlation dimension method works usually with an embedding space of dimension m. We see here two serious problems: 1) for given data, how to choose the embedding space; and 2) what is the accuracy of the characteristics D₂ obtained from the embedded data. The problems are illustrated considering time series of 5 French stock data, for which, despite all the restraints, we obtain reasonable results permitting to distinguish between stocks differentiated dynamics.