  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.
