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

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.