  Bid-ask spread is taken as an important measure of the financial market
liquidity. In this article, we study the dynamics of the spread return and the
spread volatility of four liquid stocks in the Chinese stock market, including
the memory effect and the multifractal nature. By investigating the
autocorrelation function and the Detrended Fluctuation Analysis (DFA), we find
that the spread return is lack of long-range memory, while the spread
volatility is long-range time correlated. Moreover, by applying the
Multifractal Detrended Fluctuation Analysis (MF-DFA), the spread return is
observed to possess a strong multifractality, which is similar to the dynamics
of a variety of financial quantities. Differently from the spread return, the
spread volatility exhibits a weak multifractal nature.
