EURO 2024 Copenhagen
Abstract Submission

EURO-Online login

1493. Waveform Dictionary Matching Pursuit for Denoising Step Function Signals in Finance

Invited abstract in session TA-63: Models for Financial Data and Risk Management, stream OR in Banking, Finance and Insurance: New Tools for Risk Management.

Tuesday, 8:30-10:00
Room: S14 (building: 101)

Authors (first author is the speaker)

1. Pierluigi Vellucci
Dept. of Economics, Rome Tre University

Abstract


In signal analysis, noise often obscures crucial patterns in processes of interest, particularly in economic contexts where factors like liquidity trades and agent errors contribute to data distortion. Addressing this challenge involves managing noise through mathematical approaches. One common scenario arises when denoising signals characterized by step functions with numerous discontinuities, prevalent in economic and financial time series. The violation of stationarity assumptions complicates noise removal, often mischaracterizing noisy points as signal discontinuities, leading to erroneous forecasting and inference.

This paper proposes a flexible denoising approach leveraging a sparse representation framework, particularly focusing on approximating step functions using rectangular functions. The method adopts the Weak-Orthogonal Greedy Algorithm (WOGA) or matching pursuit (MP) to iteratively remove noise from step function-derived signals. By selecting elementary functions from a highly redundant set, the algorithm constructs an approximate orthogonal basis expansion of the signal, effectively capturing its discontinuities.

The paper establishes theoretical foundations for the proposed method, demonstrating its efficacy in capturing discontinuities while simplifying calculations. Specifically, theorems elucidate optimal conditions for waveform dictionary selection, facilitating efficient denoising iterations.

Keywords

Status: accepted

Back to the list of papers