# Granger-causality without assuming linear regression, enhancements to generalCorr package

[This article was first published on

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Consider the regression Y(t) =a0+a1 Y(t-1)+ .. +ap Y(t-p) +b1 X(t-1)+.. bp X(t-p) +e(t)
Let (X — g — > Y) denote that the time series X(t) Granger-causes the Y(t) series.
The R package `lmtest’ has a function grangertest() for testing (X — g — > Y). It tests the Granger non-causality Null Hypothesis H0: b1=b2= …bp=0, that certain regression coefficients are all zero.
This is a standard procedure in econometrics textbooks and assumes linear regression and the F-test. Now the F-test is correct only if the underlying distribution of regression errors e(t) is Normal. Normality a strong assumption and easily relaxed by using the bootstrap. generalCorr::bootGcRsq relaxes the Normality assumption and considers kernel regressions which provide far better fits (higher R-squares)
generalCorr::causeSummary(mtx) is a powerful tool for assessing concurrent causality not covered by Granger causality
Measures of dependence in statistics are symmetric. Why?
Dependence relations in nature or data are almost never symmetric. (a) An infant depends on mother for survival, but mother’s survival does not equally depend on the infant. (b) New York’s rainfall depends on the latitude, but latitude does not equally depend on the New York’s rainfall at all.
As a measure of dependence the 100+ year old Pearson correlation coefficient miserably underestimates dependence. For example if x=1:10 and y=sin(x) perfectly depends on x, a good measure of dependence should be 1. Instead, the Pearson correlation coefficient -0.17 under-estimates it by 83%.
The gmcmtx0(mtx) function in `generalCorr’ package provides a non-symmetric matrix of generalized correlation coefficients with the correct measure of dependence. depMeas(x,y) gives a correct measure of dependence.**R-posts.com**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Granger-causality without assuming linear regression, enhancements to generalCorr package was first posted on December 9, 2020 at 6:39 am.

©2020 “R-posts.com“. Use of this feed is for personal non-commercial use only. If you are not reading this article in your feed reader, then the site is guilty of copyright infringement. Please contact me at tal.galili@gmail.com

To

**leave a comment**for the author, please follow the link and comment on their blog:**R-posts.com**.R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.