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Correntropy-based partial directed coherence for testing multivariate Granger causality in nonlinear processes
Rohit Kannan,
Published in American Physical Society
2014
PMID: 25019761
Volume: 89
   
Issue: 6
Abstract
Identification of directional influences in multivariate systems is of prime importance in several applications of engineering and sciences such as plant topology reconstruction, fault detection and diagnosis, and neurosciences. A spectrum of related directionality measures, ranging from linear measures such as partial directed coherence (PDC) to nonlinear measures such as transfer entropy, have emerged over the past two decades. The PDC-based technique is simple and effective, but being a linear directionality measure has limited applicability. On the other hand, transfer entropy, despite being a robust nonlinear measure, is computationally intensive and practically implementable only for bivariate processes. The objective of this work is to develop a nonlinear directionality measure, termed as KPDC, that possesses the simplicity of PDC but is still applicable to nonlinear processes. The technique is founded on a nonlinear measure called correntropy, a recently proposed generalized correlation measure. The proposed method is equivalent to constructing PDC in a kernel space where the PDC is estimated using a vector autoregressive model built on correntropy. A consistent estimator of the KPDC is developed and important theoretical results are established. A permutation scheme combined with the sequential Bonferroni procedure is proposed for testing hypothesis on absence of causality. It is demonstrated through several case studies that the proposed methodology effectively detects Granger causality in nonlinear processes. © 2014 American Physical Society.
About the journal
JournalData powered by TypesetPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
PublisherData powered by TypesetAmerican Physical Society
ISSN15393755
Open AccessNo
Concepts (17)
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    Entropy
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    Fault detection
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    BONFERRONI PROCEDURE
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    CONSISTENT ESTIMATORS
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    Fault detection and diagnosis
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    GENERALIZED CORRELATION
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    PARTIAL DIRECTED COHERENCE
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    PARTIAL DIRECTED COHERENCES (PDC)
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    TOPOLOGY RECONSTRUCTION
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    VECTOR AUTOREGRESSIVE MODEL
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    Statistical tests
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    Computer simulation
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    Multivariate analysis
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    Nonlinear system
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    Statistical model
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    Logistic models
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    Nonlinear dynamics