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

## Author Info

• 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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File URL: http://arxiv.org/pdf/1311.0657
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## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1311.0657.

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Date of creation: Nov 2013
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Handle: RePEc:arx:papers:1311.0657

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Web page: http://arxiv.org/

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## References

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1. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
2. 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.
3. Ladislav Kristoufek, 2013. "Measuring correlations between non-stationary series with DCCA coefficient," Papers 1310.3984, arXiv.org.
4. 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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