Description Usage Arguments Value Author(s) References See Also Examples

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.

1 | ```
GcRsqX12c(x1, x2, px1 = 4, px2 = 4, pwanted = 4, ctrl = 0)
``` |

`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 |

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

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

Vinod, H. D. 'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, https://doi.org/gffn86

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

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