The Generalized Riemann or Henstock Integral Underpinning Multivariate Data Analysis: Application to Faint Structure Finding in Price Processes

TL;DR

This paper introduces a new generalized integral framework based on the Riemann or Henstock integral, aimed at improving multivariate data analysis by better handling pathological cases, with applications to revealing faint structures in financial data.

Contribution

It develops a novel theoretical foundation for data processing using generalized integrals, enhancing analysis robustness and applicability to complex, limit, or pathological data scenarios.

Findings

Enhanced ability to detect faint structures in financial data

Provides a rigorous mathematical basis for data encoding and analysis

Improves justification for conclusions in complex data analysis

Abstract

Practical data analysis involves many implicit or explicit assumptions about the good behavior of the data, and excludes consideration of various potentially pathological or limit cases. In this work, we present a new general theory of data, and of data processing, to bypass some of these assumptions. The new framework presented is focused on integration, and has direct applicability to expectation, distance, correlation, and aggregation. In a case study, we seek to reveal faint structure in financial data. Our new foundation for data encoding and handling offers increased justification for our conclusions.