Granger.inference.unconditional: Inference on unconditional Granger-causality

In grangers: Inference on Granger-Causality in the Frequency Domain

Description

Inference on the unconditional Granger-causality spectrum is provided generating bootstrap time series by the stationary boostrap of Politis and Romano (1994). For computational details we refer to Ding et al. (2006) and Farne' and Montanari (2018).

Usage

Granger.inference.unconditional(x, y, ic.chosen = "SC",
  max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none",
  p = 0, nboots = 1000, conf = 0.95, bp = NULL, ts_boot = 1)

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 with computed thresholds. 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.
nboots	number of bootstrap series to be computed by function tsbootstrap of package tseries. It defaults to 1000.
conf	prescribed confidence level. It defaults to 0.95.
bp	matrix containing previously simulated bootstrap series, having as rows time points, as columns variables x and y (in this order). It defaults to NULL.
ts_boot	boolean equal to 1 if the stationary bootstrap of Politis and Romano (1994) is applied, 0 otherwise. It defaults to 1.

Details

Granger.inference.unconditional provides bootstrap inference for the Granger-causality unconditional spectrum of a time series x (effect variable) respect to a time series y (cause variable). It requires packages vars and tseries.

Value

frequency: frequencies used by Fast Fourier Transform.

n: time series length.

nboots: number of bootstrap series used.

confidence_level: prescribed confidence level.

stat_yes: boolean equal to 0 if no stationary VAR is estimated across bootstrap samples, 1 otherwise.

non_stationarity_rate: percentage of non-stationary VAR models (at least one root larger than one) estimated on bootstrapped x and y.

delay_mean: mean number of delays of stationary VAR models estimated on x and y.

quantile_unconditional_causality_y.to.x: computed quantile of the Granger-causality unconditional spectrum from y to x.

quantile_unconditional_causality_x.to.y: computed quantile of the Granger-causality unconditional spectrum from x to y.

freq_y.to.x: frequencies at which the Granger-causality unconditional spectrum from y to x exceeds the computed threshold.

freq_x.to.y: frequencies at which the Granger-causality unconditional spectrum from x to y exceeds the computed threshold.

q_max_x: computed quantile of the Granger-causality unconditional spectrum from y to x under Bonferroni correction.

q_max_y: computed quantile of the Granger-causality unconditional spectrum from x to y under Bonferroni correction.

freq_max_y.to.x: frequencies at which the Granger-causality unconditional spectrum from y to x exceeds the computed threshold under Bonferroni correction.

freq_max_x.to.y: frequencies at which the Granger-causality unconditional spectrum from x to y exceeds the computed threshold under Bonferroni correction.

The result is returned invisibly if plot is TRUE.

Author(s)

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

References

Politis D. N. and Romano J. P., (1994). ”The Stationary Bootstrap”. Journal of the American Statistical Association, 89, 1303–1313.

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 and tsbootstrap.

Examples

	RealGdp.rate.ts<-euro_area_indicators[,1]
m3.rate.ts<-euro_area_indicators[,2]
	inf_uncond_m3_0.95<-Granger.inference.unconditional(RealGdp.rate.ts,m3.rate.ts,nboots=10)

Example output

Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 

grangers documentation built on June 3, 2019, 5:05 p.m.