MULTIFRACTAL MEASURES OF TIME SERIES: f(α) SURFACES

Abstract

Binning the data points of a time series and associating a contraction map with each bin gives rise to a driven IFS representation of the time series. Varying the bins changes the driven IFS, sometimes in complex ways difficult to parse. From the transition matrix for any particular binning we can plot an f(α) curve. Assembling these curves as the bins change gives a surface, which we call the f(α) surface. We use properties of this surface to investigate time series from iterating logistic and tent maps, and also time series of financial data.