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Measuring correlations between non-stationary series with DCCA coefficient

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  • Ladislav Kristoufek

Abstract

In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured by the fractional differencing parameter $d$). For a comparison, we also report the results for the standard Pearson's correlation coefficient. The DCCA coefficient dominates the Pearson's coefficient for non-stationary series.

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  • Ladislav Kristoufek, 2013. "Measuring correlations between non-stationary series with DCCA coefficient," Papers 1310.3984, arXiv.org.
    • Handle: RePEc:arx:papers:1310.3984
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    1. Ladislav Kristoufek, 2013. "Testing power-law cross-correlations: Rescaled covariance test," Papers 1307.4727, arXiv.org, revised Aug 2013.
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    13. 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.
    14. 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.
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    16. Zebende, G.F. & Filho, A. Machado, 2009. "Cross-correlation between time series of vehicles and passengers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4863-4866.
    17. Podobnik, Boris & Horvatic, Davor & Lam Ng, Alfonso & Eugene Stanley, H. & Ivanov, Plamen Ch., 2008. "Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3954-3959.
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    19. Vassoler, R.T. & Zebende, G.F., 2012. "DCCA cross-correlation coefficient apply in time series of air temperature and air relative humidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2438-2443.
    20. Hajian, S. & Movahed, M. Sadegh, 2010. "Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4942-4957.
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    2. da Silva, Marcus Fernandes & Leão Pereira, Éder Johnson de Area & da Silva Filho, Aloisio Machado & Nunes de Castro, Arleys Pereira & Miranda, José Garcia Vivas & Zebende, Gilney Figueira, 2015. "Quantifying cross-correlation between Ibovespa and Brazilian blue-chips: The DCCA approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 124-129.
    3. Zhang, Wei & Wang, Pengfei & Li, Xiao & Shen, Dehua, 2018. "Quantifying the cross-correlations between online searches and Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 657-672.
    4. Ferreira, Paulo & Loures, Luís & Nunes, José & Brito, Paulo, 2018. "Are renewable energy stocks a possibility to diversify portfolios considering an environmentally friendly approach? The view of DCCA correlation coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 675-681.
    5. Stefano Ferretti, 2023. "On the Modeling and Simulation of Portfolio Allocation Schemes: an Approach Based on Network Community Detection," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 969-1005, October.
    6. Li, Jianxuan & Shi, Yingying & Cao, Guangxi, 2018. "Topology structure based on detrended cross-correlation coefficient of exchange rate network of the belt and road countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1140-1151.
    7. Zhang, Wei & Wang, Pengfei & Li, Xiao & Shen, Dehua, 2018. "The inefficiency of cryptocurrency and its cross-correlation with Dow Jones Industrial Average," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 658-670.
    8. Kristoufek, Ladislav, 2014. "Leverage effect in energy futures," Energy Economics, Elsevier, vol. 45(C), pages 1-9.
    9. Erdem, Orhan & Ceyhan, Elvan & Varli, Yusuf, 2014. "A new correlation coefficient for bivariate time-series data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 274-284.
    10. Zhang, Wei & Li, Yi & Zhang, Zuochao & Shen, Dehua, 2018. "The dynamic cross-correlations between foreign news, local news and stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 861-872.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Nascimento Filho, A.S. & Pereira, E.J.A.L. & Ferreira, Paulo & Murari, T.B. & Moret, M.A., 2018. "Cross-correlation analysis on Brazilian gasoline retail market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 550-557.

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