Granger.conditional {grangers}

Conditional Granger-causality estimation

Description

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).

Usage

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

Arguments

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.

Details

⁠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.

Value

⁠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.

Author(s)

Matteo Farne', [e-mail]

References

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.

See Also

VAR.

Examples

	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)