Local Linear Dependence Measure for Functionally Correlated Variables

Loann Desboulets and Costin Protopopescu ()
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Costin Protopopescu: Aix-Marseille Univ., CNRS, EHESS, Centrale Marseille, AMSE, https://www.amse-aixmarseille.fr/users/protopopescu

No 1853, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: We propose a new correlation measure for functionally correlated variables based on local linear dependence. It is able to detect non-linear, non-monotonic and even implicit relationships. Applying the classical linear correlation in a local framework combined with tools from Principal Components Analysis the statistic is capable of detecting very complex dependences among the data. In a first part we prove that it meets the properties of independence, similarity invariance and dependence and the axiom of continuity. In a second part we run a numerical simulation over a variety of dependences and compare it to other dependence measures in the literature. The results indicate that we outperform existing coefficients. We also show better stability and robustness to noise.

Keywords: local correlation; Pearson coefficient; PCA; non-parametric statistic; implicit dependence; non-monotonic; non-linear (search for similar items in EconPapers)
Pages: 17 pages
Date: 2018-11
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:aim:wpaimx:1853

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