Long-range memory test by the burst and inter-burst duration distribution

TL;DR

This paper introduces a burst and inter-burst duration analysis method to reliably assess long-range memory in financial market order flow, outperforming traditional estimators and providing consistent Hurst exponent evaluations.

Contribution

It proposes a new statistical test based on burst durations to evaluate long-range memory, demonstrating its reliability over existing methods using order book data.

Findings

The method provides more consistent Hurst exponent estimates.

It outperforms traditional estimators in reliability.

Applicable across different stocks and time definitions.

Abstract

It is empirically established that order flow in the financial markets is positively auto-correlated and can serve as an example of a social system with long-range memory. Nevertheless, widely used long-range memory estimators give varying values of the Hurst exponent. We propose the burst and inter-burst duration statistical analysis as one more test of long-range memory and implement it with the limit order book data comparing it with other widely used estimators. This method gives a more reliable evaluation of the Hurst exponent independent of the stock in consideration or time definition used. Results strengthen the expectation that burst and inter-burst duration analysis can serve as a better method to investigate the property of long-range memory.