# GcRsqX12c: Generalized Granger-Causality. If dif>0, x2 Granger-causes... In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

 GcRsqX12c R Documentation

## Generalized Granger-Causality. If dif>0, x2 Granger-causes x1.

### Description

The usual Granger-causality assumes linear regressions. This allows nonlinear nonparametric kernel regressions using a local constat (lc) option. Calls GcRsqYXc for R square from kernel regression. R^2[x1=f(x1,x2)] choosing GcRsqYXc(y=x1, x=x2). The name ‘c’ in the function refers to local constant option of kernel regressions.' It predicts x1 from both x1 and x2 using all information till time (t-1). It also calls GcRsqYXc again after flipping x1 and x2. It returns RsqX1onX2, RsqX2onX1 and the difference dif=(RsqX1onX2-RsqX2onX1) If (dif>0) the regression x1=f(x1,x2) is better than the flipped version implying that x1 is more predictable or x2 Granger-causes x1 x2 –> x1, rather than vice versa. The kernel regressions use regtype="lc" for local constant, bwmethod="cv.ls" for least squares-based bandwidth selection.

### Usage

``````GcRsqX12c(x1, x2, px1 = 4, px2 = 4, pwanted = 4, ctrl = 0)
``````

### Arguments

 `x1` The data vector x1 `x2` The data vector x2 `px1` number of lags of x1 in the data default px1=4 `px2` number of lags of x2 in the data, default px2=4 `pwanted` number of lags of both x2 and x1 wanted for Granger causal analysis, default =4 `ctrl` data matrix for designated control variable(s) outside causal paths default=0 means no control variables are present

### Value

This function returns 3 numbers: RsqX1onX2, RsqX2onX1 and dif

returns a list of 3 numbers. RsqX1onX2=(Rsquare of kernel regression of X1 on X1 and X2), RsqX2onX1= (Rsquare of kernel regression of x2 on X2 and X1), and the difference between the two Rquares called dif

### Author(s)

Prof. H. D. Vinod, Economics Dept., Fordham University, NY.

### References

Vinod, H. D. 'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/03610918.2015.1122048")}

Vinod, H. D. 'New exogeneity tests and causal paths,' Chapter 2 in 'Handbook of Statistics: Conceptual Econometrics Using R', Vol.32, co-editors: H. D. Vinod and C.R. Rao. New York: North Holland, Elsevier Science Publishers, 2019, pp. 33-64.

Vinod, H. D. Causal Paths and Exogeneity Tests in Generalcorr Package for Air Pollution and Monetary Policy (June 6, 2017). Available at SSRN: https://www.ssrn.com/abstract=2982128

Zheng, S., Shi, N.-Z., Zhang, Z., 2012. Generalized measures of correlation for asymmetry, nonlinearity, and beyond. Journal of the American Statistical Association 107, 1239-1252. -at-note internal routine

`causeSummary`

`GcRsqYXc`

### Examples

``````

## Not run:
library(Ecdat);options(np.messages=FALSE);attach(data.frame(MoneyUS))
GcRsqX12c(y,m)

## End(Not run)

``````

generalCorr documentation built on May 1, 2023, 9:06 a.m.