A Topological Approach to Scaling in Financial Data

TL;DR

This paper introduces a topological method to analyze financial data, focusing on the decomposition of price series into components of total variation to study their scaling properties, offering an alternative to traditional wavelet and Fourier techniques.

Contribution

It presents a novel topological approach for characterizing financial time series, emphasizing total variation decomposition for scaling analysis.

Findings

Topological methods effectively capture scaling in financial data.

Total variation decomposition reveals fractal-like properties.

Approach complements existing wavelet and Fourier analyses.

Abstract

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.