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

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  • Ladislav Kristoufek

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 $\rho_{DMCA}(\lambda)$ with a moving average window length $\lambda$. 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 $\rho_{DMCA}(\lambda)$ 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.

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  • Ladislav Kristoufek, 2013. "Detrending moving-average cross-correlation coefficient: Measuring cross-correlations between non-stationary series," Papers 1311.0657, arXiv.org.
    • Handle: RePEc:arx:papers:1311.0657
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    References listed on IDEAS

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    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.
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    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.
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    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.
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    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.
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    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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Kristoufek, Ladislav, 2014. "Leverage effect in energy futures," Energy Economics, Elsevier, vol. 45(C), pages 1-9.
    4. 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.
    5. Ladislav Kristoufek, 2016. "Power-law cross-correlations estimation under heavy tails," Papers 1602.05385, arXiv.org, revised Apr 2016.
    6. Ladislav Kristoufek, 2018. "Power-law cross-correlations: Issues, solutions and future challenges," Papers 1806.01616, arXiv.org.
    7. Baumöhl, Eduard, 2019. "Are cryptocurrencies connected to forex? A quantile cross-spectral approach," Finance Research Letters, Elsevier, vol. 29(C), pages 363-372.
    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.

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