Introduction of L0 norm and application of L1 and C1 norm in the study of time-series

TL;DR

This paper introduces an L0 norm and applies L1 and C1 norms within Topological Data Analysis to study various financial markets, highlighting the strengths and weaknesses of current TDA tools.

Contribution

The paper defines a new L0 norm and demonstrates its application alongside C1 and L1 norms in analyzing financial time-series data using TDA.

Findings

L0 norm provides new insights into market data

C1 and L1 norms complement the analysis effectively

TDA tools reveal strengths and weaknesses in market predictions

Abstract

Four markets are considered: Cryptocurrencies / South American exchange rate / Spanish Banking indices and European Indices and studied using TDA (Topological Data Analysis) tools. These tools are used to predict and showcase both strengths and weakness of the current TDA tools. In this paper a new tool $L0$ norm is defined and complemented with the already existing $C1$ norm.