Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets

TL;DR

This paper investigates long-range memory in financial markets by analyzing empirical Forex data, focusing on burst and inter-burst durations, and finds results consistent with one-dimensional stochastic processes.

Contribution

It provides empirical evidence supporting the use of burst duration statistics to test for long-range memory in financial time series, aligning with non-linear stochastic models.

Findings

Power-law exponents near 3/2 for burst durations

Results consistent with one-dimensional stochastic process

Supports agent-based herding model explanations

Abstract

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading activity time series from the Forex. From the empirical time series we obtain probability density functions of burst and inter-burst duration. Our analysis reveals that the power-law exponents of the obtained probability density functions are close to $3/2$, which is a characteristic feature of the one-dimensional stochastic processes. This is in a good agreement with earlier proposed model of absolute return based on the non-linear stochastic differential equations derived from the agent-based herding model.