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

ArXiv ID: 2401.05423 “View on arXiv”

Authors: Unknown

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.

Keywords: Topological Data Analysis (TDA), L0 norm, C1 norm, Market prediction, Shape analysis, Multiple (Cryptocurrencies, Forex, Indices)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper introduces and applies advanced topological mathematics (TDA, homology, persistence landscapes) with dense theoretical exposition, but the empirical validation relies on visual inspection of a few specific market examples without statistical testing, out-of-sample validation, or code/implementation details.

  flowchart TD
    A["Research Goal:<br/>New TDA tools for market prediction"] --> B["Data Collection:<br/>4 Markets: Crypto, Latam FX, Spanish Banks, EU Indices"]
    B --> C["Methodology:<br/>Topological Data Analysis - TDA"]
    C --> D["Computational Process:<br/>Define & Apply L0 norm<br/>Complement with C1 norm"]
    D --> E["Key Findings:<br/>L0 + C1 norms predict market trends<br/>Reveals TDA strengths & weaknesses"]