Abstract

Granger causality has been employed to investigate causality relations between components of

stationary multiple time series. We generalize this concept by developing statistical inference

for local Granger causality for multivariate locally stationary processes.

Our proposed local

Granger causality approach captures time-evolving causality relationships in nonstationary processes. The proposed local Granger causality is well represented in the frequency domain and

estimated based on the parametric time-varying spectral density matrix using the local Whittle

likelihood. Under regularity conditions, we demonstrate that the estimators converge to multivariate normal in distribution. Additionally, the test statistic for the local Granger causality is

shown to be asymptotically distributed as a quadratic form of a multivariate normal distribution. For practical demonstration, the proposed local Granger causality method uncovered new

functional connectivity relationships between channels in brain signals. Moreover, the method

was applicable to topological data analysis to identify structural changes in financial data.

Information

Preprint No.SS-2023-0317
Manuscript IDSS-2023-0317
Complete AuthorsYan Liu, Masanobu Taniguchi, Hernando Ombao
Corresponding AuthorsYan Liu
Emailsliu@waseda.jp

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Acknowledgments

The authors would like to thank the two anonymous referees for their constructive

suggestions. This paper has benefited considerably from those comments. The first author gratefully acknowledge JSPS Grant-in-Aid for Young Scientists (B) 17K12652 and

JSPS Grant-in-Aid for Scientific Research (C) 20K11719. The second author gratefully

acknowledge JSPS Grant-in-Aid for Scientific Research (S) 18H05290 The third author

gratefully acknowledge the KAUST Research Fund. The first two authors also would

like to express their thanks to the Institute for Mathematical Science (IMS), Waseda

University, for their support for this research.

Supplementary Materials

The online supplementary materials provide some technical parts of the paper due to

the space limit.

Supplementary materials are available for download.