  There is a large body of work, built on tools developed in mathematics and
physics, demonstrating that financial market prices exhibit self-similarity at
different scales. In this paper, we explore the use of analytical topology to
characterize financial price series. While wavelet and Fourier transforms
decompose a signal into sets of wavelets and power spectrum respectively, the
approach presented herein decomposes a time series into components of its total
variation. This property is naturally suited for the analysis of scaling
characteristics in fractals.
