On Determining the Dimension of Real-Time Stock-Price Data.

The authors estimate the dimension of high-frequency stock-price data using the correlation integral of P. Grassberger and I. Procaccia. The data, even after filtering, appear to be of low dimension. To control for dependence in higher moments, the authors use a new technique known as the method of delays in their reconstruction. Delaying the data leads dimension estimates similar to random processes. They conclude that the data are either of low dimension with high entropy or nonlinear but of high dimension.