Activity spectrum from waiting-time distribution

TL;DR

This paper investigates the spectral properties of waiting times between trades in high-frequency financial data, employing numerical inversion of Laplace transforms and approximation methods to analyze the underlying processes.

Contribution

It introduces a novel approach to analyze waiting-time spectra in financial data using Tikhonov regularization and delta function approximations.

Findings

Spectral analysis reveals characteristics of waiting-time distributions.

Regularization method effectively inverts Laplace transforms for spectral estimation.

Approximate methods provide quick insights into waiting-time spectra.

Abstract

In high frequency financial data not only returns but also waiting times between trades are random variables. In this work, we analyze the spectra of the waiting-time processes for tick-by-tick trades. The numerical problem, strictly related with the real inversion of Laplace transforms, is analyzed by using Tikhonov's regularization method. We also analyze these spectra by a rough method using a comb of Dirac's delta functions.