Long-range Auto-correlations in Limit Order Book Markets: Inter- and Cross-event Analysis

TL;DR

This study analyzes ultra-high frequency order book data from NASDAQ Nordic over three years, revealing strong long-range correlations in inter- and cross-event durations and their dependence on time scale and economic variables.

Contribution

It provides the first detailed empirical evidence of long-range correlations in high-frequency order book events across multiple stocks and variables using DFA.

Findings

Long-range correlations are consistent across stocks and variables.

Correlation strength increases over longer time scales from hours to months.

Scaling exponents relate to economic variables, especially in inter-trade times.

Abstract

Long-range correlation in financial time series reflects the complex dynamics of the stock markets driven by algorithms and human decisions. Our analysis exploits ultra-high frequency order book data from NASDAQ Nordic over a period of three years to numerically estimate the power-law scaling exponents using detrended fluctuation analysis (DFA). We address inter-event durations (order to order, trade to trade, cancel to cancel) as well as cross-event durations (time from order submission to its trade or cancel). We find strong evidence of long-range correlation, which is consistent across different stocks and variables. However, given the crossovers in the DFA fluctuation functions, our results indicate that the long-range correlation in inter-event durations becomes stronger over a longer time scale, i.e., when moving from a range of hours to days and further to months. We also observe interesting associations between the scaling exponent and a number of economic variables, in particular, in the inter-trade time series.