Paper: arXiv 2301.13255

Authors: Nathan Zavanelli

Abstract

The method of element analysis is proposed here as an alternative to traditional wavelet-based approaches to analyzing perturbations in financial signals by scale. In this method, the processes that generate oscillations in financial signals are modelled as scaled, shifted, and isolated events that produce ripples of various frequencies across a sea of noise as opposed to a simple sinusoidal or mixed frequency oscillation or an impulse. This allows one to directly estimate the wavelet parameters derived only from the generating functions, rejecting spurious perturbations driven by noise or extraneous factors. Financial signals may then be reconstructed based on a finite set of generators localized in time and frequency. This method offers a marked advantage compared to traditional econometric tools because it directly targets the generators of oscillations. Furthermore, the choice of the Morse wavelet allows for wide latitude in capturing a broad set of diverse generators. In this work, the basic mathematical principles underlying element analysis are presented, and the method is applied to the study of variance in financial data, where the advantages of element analysis over traditional wavelet techniques is demonstrated. Specifically, in the example analysis of inflation expectations, element analysis shows a clear ability to distinguish between oscillations formed by noise and those formed by generators logically matched to historical events.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces an innovative theoretical framework using element analysis and Morse wavelets to isolate generating processes of financial oscillations from noise. While mathematically interesting and novel, the empirical application is limited to a single illustrative example (inflation expectations) without extensive backtesting or benchmark comparisons.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Financial Oscillations & Reject Noise via Element Analysis] --> B[Data Input: Financial Time Series / Inflation Expectations]
    B --> C[Methodology: Model Signals as Scaled & Shifted Generating Events]
    C --> D[Signal Processing: Apply Morse Wavelet to Extract Generator Parameters]
    D --> E[Reconstruction: Rebuild Signal from Finite Time-Frequency Generators]
    E --> F[Key Outcome: Superior Variance Estimation & Distinction of Historical Events from Noise]