Granger.unconditional {grangers}

Unconditional Granger-causality estimation

Description

Unconditional Granger-causality spectrum was first defined in Geweke (1982). It measures the strength of the causal link from time series ⁠y⁠ to time series ⁠x⁠ and viceversa in the frequency domain. It needs to estimate a VAR model on ⁠x⁠ and ⁠y⁠ by package vars. For computational details we refer to Ding et al. (2006).

Usage

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

Arguments

x

univariate time series.

y

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 unconditional Granger-causality spectra on both directions. Defaults to FALSE.

type.chosen

parameter ⁠type⁠ to be passed to function VAR. Defaults to ⁠''none''⁠. Alternatives are ⁠c(''none'',''const'',''trend'')⁠.

p

parameter ⁠p⁠ to be passed to function VAR. Defaults to 0.

Details

⁠Granger.unconditional⁠ calculates the Granger-causality unconditional spectrum of a time series ⁠x⁠ (effect 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.

⁠Unconditional_causality_y.to.x⁠: computed unconditional Granger-causality from ⁠y⁠ to ⁠x⁠.

⁠Unconditional_causality_x.to.y⁠: computed unconditional Granger-causality from ⁠x⁠ to ⁠y⁠.

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

The result is returned invisibly if plot is TRUE.

Author(s)

Matteo Farne', Angela Montanari, [e-mail]

References

Geweke, J., 1982. Measurement of linear dependence and feedback between multiple time series. J. Am. Stat. Assoc. 77, 304–313.

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]
uncond_m3<-Granger.unconditional(RealGdp.rate.ts,m3.rate.ts,"SC",4)