Granger causality

Problem Description of Granger causality

Granger causality Detection’s task is to find out the Granger causality lies in multi-channel time series on window level or channel level, like this:

../_images/GC_show1.png
../_images/GC_show2.png

To formalize, give a time series with multi channels:

../_images/gc-1.png

We aim to find the Granger causality lies in channel level:

../_images/gc-2.png

We also try to pinpoint causality from the channel level to the point-to-point level:

../_images/gc-3.png

where 2 time points are in the same window index.

Models of Granger causality

Abbr

Algorithm

level

supervise

Year

Class

Ref

GC

Granger causality

channel level

unsupervised

1969

realseries.models.GC.GC

[GC]

DWGC

Dynamic window-level Granger causality

window level

unsupervised

2020(original)

realseries.models.DWGC.DWGC

[DWGC]

References

GC

Clive WJ Granger. Investigating causal relations by econometric models and cross-spectral methods. Econometrica: journal of the Econometric Society, pages 424–438, 1969.

DWGC

Dynamic Window-level Granger Causality of Multi-channel Time Series. Zhiheng Zhang, Wenbo Hu, Tian Tian, Jun Zhu. arXiv:2006.07788. 2020.