Granger causality

Today in class, Granger causality was mentioned briefly. Since today’s lecture was primarily based on what causation really is, I thought I would look more into exactly what Granger causality is. By definition, Granger causality is a statistical hypothesis test that is used to determine if one thing is useful in predicting another. G-causality is typically tested in the context of linear regression models. Below is an illustration of this:

X 1 (t)=∑ j=1 p A 11,j X 1 (t−j)+∑ j=1 p A 12,j X 2 (t−j)+E 1 (t)

X 2 (t)=∑ j=1 p A 21,j X 1 (t−j)+∑ j=1 p A 22,j X 2 (t−j)+E 2 (t) (1)

P=the maximum # of lagged observations included in the model order

Although these formulas are not something we will be using, I think they are interesting to look at. As I was reading more about G-causalities, I found that they have been used a lot more in recent years in regards to the field of neuroscience. Being one that is interested in this field, I found this intriguing. The use of the G-causality is to identify causal interactions in neural data. For example, in 2001 Kaminski et al. noted increasing anterior to posterior causal influences during the transition of waking to sleep by the use of EEG signals. G-causality has even been used to see the relationship between neuro-anatomy, network dynamics, and behavior. Overall, I thought this was an interesting technique that many people use. 

http://www.scholarpedia.org/article/Granger_causality