IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v406y2014icp169-175.html
   My bibliography  Save this article

Detrending moving-average cross-correlation coefficient: Measuring cross-correlations between non-stationary series

Author

Listed:
  • Kristoufek, Ladislav

Abstract

In the paper, we introduce a new measure of correlation between possibly non-stationary series. As the measure is based on the detrending moving-average cross-correlation analysis (DMCA), we label it as the DMCA coefficient ρDMCA(λ) with a moving average window length λ. We analytically show that the coefficient ranges between −1 and 1 as a standard correlation does. In the simulation study, we show that the values of ρDMCA(λ) very well correspond to the true correlation between the analyzed series regardless the (non-)stationarity level. Dependence of the newly proposed measure on other parameters–correlation level, moving average window length and time series length–is discussed as well.

Suggested Citation

  • Kristoufek, Ladislav, 2014. "Detrending moving-average cross-correlation coefficient: Measuring cross-correlations between non-stationary series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 169-175.
    • Handle: RePEc:eee:phsmap:v:406:y:2014:i:c:p:169-175
    DOI: 10.1016/j.physa.2014.03.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711400209X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.03.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. He, Ling-Yun & Chen, Shu-Peng, 2011. "A new approach to quantify power-law cross-correlation and its application to commodity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3806-3814.
    2. Barunik, Jozef & Kristoufek, Ladislav, 2010. "On Hurst exponent estimation under heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3844-3855.
    3. Kristoufek, Ladislav, 2014. "Measuring correlations between non-stationary series with DCCA coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 291-298.
    4. Serinaldi, Francesco, 2010. "Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2770-2781.
    5. Zhi-Qiang Jiang & Wei-Xing Zhou, 2011. "Multifractal detrending moving average cross-correlation analysis," Papers 1103.2577, arXiv.org, revised Mar 2011.
    6. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    7. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
    8. Zebende, G.F. & da Silva, M.F. & Machado Filho, A., 2013. "DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1756-1761.
    9. Schumann, Aicko Y. & Kantelhardt, Jan W., 2011. "Multifractal moving average analysis and test of multifractal model with tuned correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2637-2654.
    10. Ladislav Kristoufek, 2012. "Multifractal Height Cross-Correlation Analysis: A New Method for Analyzing Long-Range Cross-Correlations," Papers 1201.3473, arXiv.org, revised Jan 2012.
    11. Sergio Arianos & Anna Carbone, 2008. "Cross-correlation of long-range correlated series," Papers 0804.2064, arXiv.org, revised Mar 2009.
    12. Zebende, G.F., 2011. "DCCA cross-correlation coefficient: Quantifying level of cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 614-618.
    13. Gao-Feng Gu & Wei-Xing Zhou, 2010. "Detrending moving average algorithm for multifractals," Papers 1005.0877, arXiv.org, revised Jun 2010.
    14. Ying-Hui Shao & Gao Feng Gu & Zhi-Qiang Jiang & Wei-Xing Zhou & Didier Sornette, 2012. "Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series," Papers 1208.4158, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Qin, Jing & Ge, Jintian & Lu, Xinsheng, 2018. "The effectiveness of the monetary policy in China: New evidence from long-range cross-correlation analysis and the components of multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1026-1037.
    2. Kristoufek, Ladislav, 2014. "Leverage effect in energy futures," Energy Economics, Elsevier, vol. 45(C), pages 1-9.
    3. Ladislav Kristoufek & Paulo Ferreira, 2018. "Capital asset pricing model in Portugal: Evidence from fractal regressions," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 17(3), pages 173-183, November.
    4. Baumöhl, Eduard, 2019. "Are cryptocurrencies connected to forex? A quantile cross-spectral approach," Finance Research Letters, Elsevier, vol. 29(C), pages 363-372.
    5. Kristoufek, Ladislav, 2015. "Power-law correlations in finance-related Google searches, and their cross-correlations with volatility and traded volume: Evidence from the Dow Jones Industrial components," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 194-205.
    6. Ladislav Kristoufek, 2016. "Power-law cross-correlations estimation under heavy tails," Papers 1602.05385, arXiv.org, revised Apr 2016.
    7. Ladislav Kristoufek, 2018. "Power-law cross-correlations: Issues, solutions and future challenges," Papers 1806.01616, arXiv.org.
    8. Wang, Luo-Qing & Xu, Yong-Xiang, 2018. "Assessing the relevance of individual characteristics for the structure of similarity networks in new social strata in Shanghai," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 881-889.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kristoufek, Ladislav, 2015. "Finite sample properties of power-law cross-correlations estimators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 513-525.
    2. Kristoufek, Ladislav, 2014. "Leverage effect in energy futures," Energy Economics, Elsevier, vol. 45(C), pages 1-9.
    3. Kristoufek, Ladislav, 2015. "Power-law correlations in finance-related Google searches, and their cross-correlations with volatility and traded volume: Evidence from the Dow Jones Industrial components," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 194-205.
    4. Shen, Chenhua, 2017. "A comparison of principal components using TPCA and nonstationary principal component analysis on daily air-pollutant concentration series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 453-464.
    5. repec:arx:papers:1501.02947 is not listed on IDEAS
    6. Kristoufek, Ladislav, 2014. "Measuring correlations between non-stationary series with DCCA coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 291-298.
    7. Kristoufek, Ladislav, 2015. "Can the bivariate Hurst exponent be higher than an average of the separate Hurst exponents?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 124-127.
    8. Qin, Jing & Ge, Jintian & Lu, Xinsheng, 2018. "The effectiveness of the monetary policy in China: New evidence from long-range cross-correlation analysis and the components of multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1026-1037.
    9. Liu, Li & Wang, Yudong, 2014. "Cross-correlations between spot and futures markets of nonferrous metals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 20-30.
    10. Zebende, G.F. & da Silva, M.F. & Machado Filho, A., 2013. "DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1756-1761.
    11. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Casado Belmonte, M.P. & Trinidad Segovia, J.E., 2020. "A note on power-law cross-correlated processes," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    12. Cao, Guangxi & Xu, Longbing & Cao, Jie, 2012. "Multifractal detrended cross-correlations between the Chinese exchange market and stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4855-4866.
    13. Kristoufek, Ladislav, 2013. "Mixed-correlated ARFIMA processes for power-law cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6484-6493.
    14. Wang, Gang-Jin & Xie, Chi & He, Ling-Yun & Chen, Shou, 2014. "Detrended minimum-variance hedge ratio: A new method for hedge ratio at different time scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 70-79.
    15. Gulich, Damián & Zunino, Luciano, 2014. "A criterion for the determination of optimal scaling ranges in DFA and MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 17-30.
    16. Zhuang, Xiaoyang & Wei, Yu & Ma, Feng, 2015. "Multifractality, efficiency analysis of Chinese stock market and its cross-correlation with WTI crude oil price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 101-113.
    17. Manimaran, P. & Narayana, A.C., 2018. "Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 228-235.
    18. Wang, Fang & Yang, Zhaohui & Wang, Lin, 2016. "Detecting and quantifying cross-correlations by analogous multifractal height cross-correlation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 954-962.
    19. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    20. Cao, Guangxi & Han, Yan & Cui, Weijun & Guo, Yu, 2014. "Multifractal detrended cross-correlations between the CSI 300 index futures and the spot markets based on high-frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 308-320.
    21. Ladislav Kristoufek, 2016. "Power-law cross-correlations estimation under heavy tails," Papers 1602.05385, arXiv.org, revised Apr 2016.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:406:y:2014:i:c:p:169-175. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.