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

Maximum entropy bootstrap (meboot) package is used for statistical inference The bootstrap output can be analyzed to estimate an approximate confidence interval on sample-based direction of the causal path. The LC in the function name stands for local constant. Kernel regression np package options regtype="lc" for local constant, and bwmethod="cv.ls" for least squares-based bandwidth selection are fixed.

1 | ```
bootGcLC(x1, x2, px2 = 4, px1 = 4, pwanted = 4, ctrl = 0, n999 = 9)
``` |

`x1` |
The data vector x1 |

`x2` |
The data vector x2 |

`px2` |
number of lags of x2 in the data, default px2=4 |

`px1` |
number of lags of x1 in the data default px1=4 |

`pwanted` |
number of lags of both x2 and x1 wanted for Granger causal analysis, default =4 |

`ctrl` |
data matrix having control variable(s) if any |

`n999` |
Number of bootstrap replications (default=9) |

out is n999 X 3 matrix for 3 outputs of GcauseX12 resampled

This computation is computer intensive and generally very slow. It may be better to use this function it at a later stage in the investigation, after a preliminary causal determination is already made. The 3 outputs of GauseX12 are two Rsquares and the difference between after subtracting the second from the first. Col. 1 has (RsqX1onX2) Col.2 has (RsqX2onX1), and Col.3 has dif=(RsqX1onX2 -RsqX2onX1) Note that R-squares are always positive. If dif>0, RsqX1onX2>RsqX2onX1, implying that x2 on RHS performs better that is, x2 –> x1 is the path, or x2 Granger-causes x1. If dif<0, x1 –> x2 holds. If dif is too close to zero, we may have bidirectional causality x1 <–> x2. The proportion of resamples (out of n999) having dif<0 suggests level of confidence in the conclusion x1 –> x2. The proportion of resamples (out of n999) having dif>0 suggests level of confidence in the conclusion x2 –> x1.

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

Zheng, S., Shi, N.-Z., and Zhang, Z. (2012). Generalized measures of correlation for asymmetry, nonlinearity, and beyond. Journal of the American Statistical Association, vol. 107, pp. 1239-1252.

Vinod, H. D. and Lopez-de-Lacalle, J. (2009). 'Maximum entropy bootstrap for time series: The meboot R package.' Journal of Statistical Software, Vol. 29(5), pp. 1-19.

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

See Also `GcRsqX12c`

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