  The statistical properties of the bid-ask spread of a frequently traded
Chinese stock listed on the Shenzhen Stock Exchange are investigated using the
limit-order book data. Three different definitions of spread are considered
based on the time right before transactions, the time whenever the highest
buying price or the lowest selling price changes, and a fixed time interval.
The results are qualitatively similar no matter linear prices or logarithmic
prices are used. The average spread exhibits evident intraday patterns
consisting of a big L-shape in morning transactions and a small L-shape in the
afternoon. The distributions of the spread with different definitions decay as
power laws. The tail exponents of spreads at transaction level are well within
the interval $(2,3)$ and that of average spreads are well in line with the
inverse cubic law for different time intervals. Based on the detrended
fluctuation analysis, we found the evidence of long memory in the bid-ask
spread time series for all three definitions, even after the removal of the
intraday pattern. Using the classical box-counting approach for multifractal
analysis, we show that the time series of bid-ask spread does not possess
multifractal nature.
