Volume 112, Number 4, November 2015
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||01 December 2015|
Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies
1 Faculty of Mathematics and Natural Sciences, University of Rzeszów - Rzeszów, Poland
2 Institute of Nuclear Physics, Polish Academy of Sciences - ul. Radzikowskiego 152, Kraków, Poland
3 Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology - Kraków, Poland
Received: 16 October 2015
Accepted: 9 November 2015
We consider a few quantities that characterize trading on a stock market in a fixed time interval: logarithmic returns, volatility, trading activity (i.e., the number of transactions), and volume traded. We search for the power-law cross-correlations among these quantities aggregated over different time units from 1 min to 10 min. Our study is based on empirical data from the American stock market consisting of tick-by-tick recordings of 31 stocks listed in Dow Jones Industrial Average during the years 2008–2011. Since all the considered quantities except the returns show strong daily patterns related to the variable trading activity in different parts of a day, which are the most evident in the autocorrelation function, we remove these patterns by detrending before we proceed further with our study. We apply the multifractal detrended cross-correlation analysis with sign preserving (MFCCA) and show that the strongest power-law cross-correlations exist between trading activity and volume traded, while the weakest ones exist (or even do not exist) between the returns and the remaining quantities. We also show that the strongest cross-correlations are carried by those parts of the signals that are characterized by large and medium variance. Our observation that the most convincing power-law cross-correlations occur between trading activity and volume traded reveals the existence of strong fractal-like coupling between these quantities.
PACS: 89.75.-k – Complex systems / 89.75.Da – Systems obeying scaling laws / 89.65.Gh – Economics; econophysics, financial markets, business and management
© EPLA, 2015
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