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Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies

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  • Rafal Rak
  • Stanislaw Drozdz
  • Jaroslaw Kwapien
  • Pawel Oswiecimka

Abstract

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 best 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.

Suggested Citation

  • Rafal Rak & Stanislaw Drozdz & Jaroslaw Kwapien & Pawel Oswiecimka, 2015. "Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies," Papers 1510.04910, arXiv.org, revised Nov 2015.
    • Handle: RePEc:arx:papers:1510.04910
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    1. Wu, Ting & Wang, Yue & Li, Ming-Xia, 2017. "Post-hit dynamics of price limit hits in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 464-471.
    2. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Pawe{l} O'swic{e}cimka & Marek Stanuszek, 2018. "Multifractal cross-correlations between the World Oil and other Financial Markets in 2012-2017," Papers 1812.08548, arXiv.org, revised Jun 2019.
    3. Meraz, M. & Alvarez-Ramirez, J. & Rodriguez, E., 2022. "Multivariate rescaled range analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    4. Wang, Jian & Huang, Menghao & Zhang, Yudong & Kim, Junseok, 2022. "Modification of multifractal analysis based on multiplicative cascade image," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    5. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    6. Gontis, V. & Kononovicius, A., 2017. "Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 266-272.
    7. Stanisław Drożdż & Ludovico Minati & Paweł Oświȩcimka & Marek Stanuszek & Marcin Wa̧torek, 2019. "Signatures of the Crypto-Currency Market Decoupling from the Forex," Future Internet, MDPI, vol. 11(7), pages 1-18, July.
    8. Hasan, Rashid & Mohammed Salim, M., 2017. "Power law cross-correlations between price change and volume change of Indian stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 620-631.
    9. Wang, Jian & Shao, Wei & Ma, Chenmin & Chen, Wenbing & Kim, Junseok, 2021. "Co-movements between Shanghai Composite Index and some fund sectors in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    10. Stosic, Dusan & Stosic, Darko & de Mattos Neto, Paulo S.G. & Stosic, Tatijana, 2019. "Multifractal characterization of Brazilian market sectors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 956-964.
    11. Lu, Xinsheng & Sun, Xinxin & Ge, Jintian, 2017. "Dynamic relationship between Japanese Yen exchange rates and market anxiety: A new perspective based on MF-DCCA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 144-161.
    12. Stanis{l}aw Dro.zd.z & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek & Marcin Wk{a}torek, 2019. "Signatures of crypto-currency market decoupling from the Forex," Papers 1906.07834, arXiv.org, revised Jul 2019.
    13. Zheng, Zeyu & Gui, Jun & Qiao, Zhi & Fu, Yang & Stanley, H.Eugene & Li, Baowen, 2019. "New dynamics between volume and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1343-1350.
    14. Sun, Xinxin & Lu, Xinsheng & Yue, Gongzheng & Li, Jianfeng, 2017. "Cross-correlations between the US monetary policy, US dollar index and crude oil market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 326-344.
    15. Oussama Tilfani & Paulo Ferreira & My Youssef El Boukfaoui, 2021. "Dynamic cross-correlation and dynamic contagion of stock markets: a sliding windows approach with the DCCA correlation coefficient," Empirical Economics, Springer, vol. 60(3), pages 1127-1156, March.
    16. Guo, Yaoqi & Shi, Fengyuan & Yu, Zhuling & Yao, Shanshan & Zhang, Hongwei, 2022. "Asymmetric multifractality in China’s energy market based on improved asymmetric multifractal cross-correlation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    17. Rodriguez, E. & Alvarez-Ramirez, J., 2021. "Time-varying cross-correlation between trading volume and returns in US stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    18. Paulo Ferreira, 2017. "Portuguese and Brazilian stock market integration: a non-linear and detrended approach," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 16(1), pages 49-63, April.
    19. Ferreira, Paulo, 2016. "Does the Euro crisis change the cross-correlation pattern between bank shares and national indexes?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 320-329.
    20. Xu, Lin & Wu, Chenyang & Qin, Quande & Lin, Xiaoying, 2022. "Spillover effects and nonlinear correlations between carbon emissions and stock markets: An empirical analysis of China's carbon-intensive industries," Energy Economics, Elsevier, vol. 111(C).
    21. Contreras-Reyes, Javier E. & Idrovo-Aguirre, Byron J., 2020. "Backcasting and forecasting time series using detrended cross-correlation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    22. Borko Stosic & Tatijana Stosic, 2024. "Dissecting Multifractal detrended cross-correlation analysis," Papers 2406.19406, arXiv.org.
    23. Li, Wei & Lu, Xinsheng & Ren, Yongping & Zhou, Ying, 2018. "Dynamic relationship between RMB exchange rate index and stock market liquidity: A new perspective based on MF-DCCA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 726-739.

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