Granger.conditional: Conditional Granger-causality estimation
In grangers: Inference on Granger-Causality in the Frequency Domain

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

Conditional Granger-causality spectrum was first defined in Geweke (1984). It measures the strength of the causal link from time series y to time series x once removed the mediating effect of z in the frequency domain. Differently from function Granger.unconditional, this function provides only the unidirectional causality from y to x. Here we need to estimate two VAR models: the first on x and z, the second on x, y, z, by package vars. Parameters specified for function VAR hold for both estimations. For computational details we refer to Ding et al. (2006).

1 2	Granger.conditional(x, y, z, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p1 = 0, p2 = 0)

`x`	univariate time series.
`y`	univariate time series (of the same length of `x`).
`z`	univariate time series (of the same length of `x`).
`ic.chosen`	estimation method parameter `ic` to be passed to function VAR of package vars. Defaults to ”SC” (Schwarz criterion). Alternatives are `c(''AIC'',''HQ'',''SC'',''FPE'')`.
`max.lag`	maximum number of lags `lag.max` to be passed to function `VAR`. Defaults to `min(4, length(x) - 1)`.
`plot`	logical; if TRUE, it returns the plot of conditional Granger-causality spectrum. Defaults to FALSE.
`type.chosen`	parameter `type` to be passed to function `VAR`. Defaults to `''none''`. Alternatives are `c(''none'',''const'',''trend'')`.
`p1`	parameter `p` to be passed to function VAR. It corresponds to the number of lags of the first VAR model. Defaults to 0.
`p2`	parameter `p` to be passed to function VAR. It corresponds to the number of lags of the second VAR model. Defaults to 0.

Granger.conditional calculates the Granger-causality conditional spectrum of a time series x (effect variable) on a time series z (conditioning variable) respect to a time series y (cause variable). It requireNamespaces package vars.

frequency: frequencies used by Fast Fourier Transform.

n: time series length.

Conditional_causality_y.to.x.on.z: computed conditional Granger-causality from y to x on z.

roots_1: the roots of the estimated VAR on x and y.

roots_2: the roots of the estimated VAR on x, y and z.

The result is returned invisibly if plot is TRUE.

Matteo Farne', matteo.farne2@unibo.it

Geweke J., 1984. Measures of conditional linear dependence and feedback between time series. J. Am. Stat. Assoc. 79, 907–915.

Ding, M., Chen, Y., Bressler, S.L., 2006. Granger Causality: Basic Theory and Application to Neuroscience, Chap.17. Handbook of Time Series Analysis Recent Theoretical Developments and Applications.

Farne', M., Montanari, A., 2018. A bootstrap test to detect prominent Granger-causalities across frequencies. <arXiv:1803.00374>, Submitted.

VAR.

	RealGdp.rate.ts<-euro_area_indicators[,1]
	m3.rate.ts<-euro_area_indicators[,2]
	hicp.rate.ts<-euro_area_indicators[,4]
	cond_m3.to.gdp.by.hicp<-
Granger.conditional(RealGdp.rate.ts,m3.rate.ts,hicp.rate.ts,"SC",4)