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Long-range correlation in financial time series reflects the complex dynamicsof the stock markets driven by algorithms and human decisions. Our analysisexploits ultra-high frequency order book data from NASDAQ Nordic over a periodof three years to numerically estimate the power-law scaling exponents usingdetrended fluctuation analysis (DFA). We address inter-event durations (orderto 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 oflong-range correlation, which is consistent across different stocks andvariables. However, given the crossovers in the DFA fluctuation functions, ourresults indicate that the long-range correlation in inter-event durationsbecomes stronger over a longer time scale, i.e., when moving from a range ofhours to days and further to months. We also observe interesting associationsbetween the scaling exponent and a number of economic variables, in particular,in the inter-trade time series.

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