GcRsqX12 {generalCorr}

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

Description

The usual Granger-causality assumes linear regressions. This function allows nonlinear nonparametric kernel regressions using a local linear (ll) option. Granger-causality (Gc) is generalized using nonlinear kernel regressions using local linear (ll) option. This functionn computes two R^2 values. (i) R12 or kernel regression R^2 of x1t on its own lags and x2t and its lags. (ii) R21 or kernel regression R^2 of x2t on its own lags and x1t and its lags. (iii) dif=R12-R21, the difference between the two R^2 values. If dif>0 then x2 Granger-causes x1.

Usage

GcRsqX12(x1, x2, px1 = 4, px2 = 4, pwanted = 4, ctrl = 0)

Arguments

x1

The data vector x1

x2

The data vector x2

px1

The number of lags of x1 in the data default px1=4

px2

The 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

Details

Calls GcRsqYX for R-square from kernel regression (local linear version) R^2[x1=f(x1,x2)] choosing GcRsqYX(y=x1, x=x2). It predicts x1 from both x1 and x2 using all information till time (t-1). It also calls GcRsqYX again after flipping x1 and x2. It returns RsqX1onX2, RsqX2onX1 and the difference dif=(RsqX1onX2-RsqX2onX1) If (dif>0) the regression y=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="ll" for local linear, bwmethod="cv.aic" for AIC-based bandwidth selection.

Value

This function returns 3 numbers: RsqX1onX2, RsqX2onX1 and dif

returns a list of 3 numbers. RsqX1onX2=(Rsquare of kernel regression of X1 on lags of X1 and X2 and its lags), RsqX2onX1= (Rsquare of kernel regression of x2 on own lags of X2 and X1), and the difference between the two Rquares (first minus second) called ‘dif.’ If dif>0 then x2 Granger-causes x1

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, 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

See Also

bootGcRsq, causeSummary, GcRsqYX.

Examples

## Not run: 
library(Ecdat);options(np.messages=FALSE);attach(data.frame(MoneyUS))
GcRsqX12(y,m)   

## End(Not run)