| Title: | Inference on Granger-Causality in the Frequency Domain |
|---|---|
| Description: | Contains five functions performing the calculation of unconditional and conditional Granger-causality spectra, and bootstrap inference on both, via the bootstrap approach of Farne' and Montanari <arXiv:1803.00374>. |
| Authors: | Matteo Farne' <[email protected]>, Angela Montanari <[email protected]> |
| Maintainer: | Matteo Farne' <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.1.0 |
| Built: | 2025-03-05 03:31:13 UTC |
| Source: | https://github.com/matfar88/grangers |
Inference on the conditional Granger-causality spectrum is provided by the parametric test of Breitung and Candelon (2006).
bc_test_cond(x, y, z, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p = 0, conf = 0.95)bc_test_cond(x, y, z, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p = 0, conf = 0.95)
x |
univariate time series. |
y |
univariate time series (of the same length of |
z |
univariate time series (of the same length of |
ic.chosen |
estimation method parameter |
max.lag |
maximum number of lags |
plot |
logical; if TRUE, it returns the plot of conditional Granger-causality spectrum. Defaults to FALSE. |
type.chosen |
parameter |
p |
parameter |
conf |
prescribed confidence level. It defaults to 0.95. |
bc_test_cond calculates the test of Breitung and Candelon (2006) on the conditional Granger-causality
of a time series x (effect variable) on a time series z (conditioning variable) respect to a time series y (cause variable).
It requires package vars.
frequency: frequencies used by Fast Fourier Transform.
n: time series length.
confidence_level: prescribed confidence level.
significant_frequencies: frequencies at which the test is significant..
F-test: computed F-test at each frequency.
F-threshold: F-threshold at each frequency under prescribed confidence level.
roots: roots of the estimated VAR model.
delays: delays of the estimated VAR model.
The result is returned invisibly if plot is TRUE.
Matteo Farne', Angela Montanari, [email protected]
Breitung, J., Candelon, B., 2006. Testing for short- and long-run causality: A frequency-domain approach. Journal of Econometrics. 132, 2, 363–378.
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_bc<-bc_test_cond(RealGdp.rate.ts,m3.rate.ts,hicp.rate.ts,ic.chosen="SC",max.lag=2)RealGdp.rate.ts<-euro_area_indicators[,1] m3.rate.ts<-euro_area_indicators[,2] hicp.rate.ts<-euro_area_indicators[,4] cond_bc<-bc_test_cond(RealGdp.rate.ts,m3.rate.ts,hicp.rate.ts,ic.chosen="SC",max.lag=2)
Inference on the unconditional Granger-causality spectrum is provided by the parametric test of Breitung and Candelon (2006).
bc_test_uncond(x, y, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p = 0, conf = 0.95)bc_test_uncond(x, y, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p = 0, conf = 0.95)
x |
univariate time series. |
y |
univariate time series (of the same length of |
ic.chosen |
estimation method parameter |
max.lag |
maximum number of lags |
plot |
logical; if TRUE, it returns the plot of conditional Granger-causality spectrum. Defaults to FALSE. |
type.chosen |
parameter |
p |
parameter |
conf |
prescribed confidence level. It defaults to 0.95. |
bc_test_uncond calculates the test of Breitung and Candelon (2006) on the unconditional Granger-causality
of a time series x (effect variable) respect to a time series y (cause variable).
It requireNamespaces package vars.
frequency: frequencies used by Fast Fourier Transform.
n: time series length.
confidence_level: prescribed confidence level.
significant_frequencies: frequencies at which the test is significant..
F-test: computed F-test at each frequency.
F-threshold: F-threshold at each frequency under prescribed confidence level.
roots: roots of the estimated VAR model.
delays: delays of the estimated VAR model.
The result is returned invisibly if plot is TRUE.
Matteo Farne', Angela Montanari, [email protected]
Breitung, J., Candelon, B., 2006. Testing for short- and long-run causality: A frequency-domain approach. Journal of Econometrics. 132, 2, 363–378.
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] uncond_bc<-bc_test_uncond(RealGdp.rate.ts,m3.rate.ts,ic.chosen="SC",max.lag=2)RealGdp.rate.ts<-euro_area_indicators[,1] m3.rate.ts<-euro_area_indicators[,2] uncond_bc<-bc_test_uncond(RealGdp.rate.ts,m3.rate.ts,ic.chosen="SC",max.lag=2)
This data set gives thre quarterly time series of real gross domestic product, M3 aggregate, M1 aggregate, inflation rate (HICP), unemployment rate and long-term interest rate for the Euro Area from Q1,1999 to Q4,2017, according to the ECB Real Time DataBase (RTDB).
euro_area_indicatorseuro_area_indicators
A matrix containing as columns six quarterly time series ranging from Q1,1999 to Q4,2017.
Documentation of the dataset 'euro_area_indicators'
ECB Real Time DataBase 'https://sdw.ecb.europa.eu/browse.do?node=9689716'.
Farne', M., Montanari, A., 2018. A bootstrap test to detect prominent Granger-causalities across frequencies. <arXiv:1803.00374>, Submitted.
Euro Area Real Time Database documentation. 'http://sdw.ecb.europa.eu/web/docu/rtdb_docu.pdf'
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).
Granger.conditional(x, y, z, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p1 = 0, p2 = 0)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 |
z |
univariate time series (of the same length of |
ic.chosen |
estimation method parameter |
max.lag |
maximum number of lags |
plot |
logical; if TRUE, it returns the plot of conditional Granger-causality spectrum. Defaults to FALSE. |
type.chosen |
parameter |
p1 |
parameter |
p2 |
parameter |
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', [email protected]
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)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)
Inference on the conditional 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).
Granger.inference.conditional(x, y, z, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p1 = 0, p2 = 0, nboots = 1000, conf = 0.95, bp = NULL, ts_boot = 1)Granger.inference.conditional(x, y, z, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p1 = 0, p2 = 0, nboots = 1000, conf = 0.95, bp = NULL, ts_boot = 1)
x |
univariate time series. |
y |
univariate time series (of the same length of |
z |
univariate time series (of the same length of |
ic.chosen |
estimation method parameter |
max.lag |
maximum number of lags |
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 |
p1 |
parameter |
p2 |
parameter |
nboots |
number of bootstrap series to be computed by function |
conf |
prescribed confidence level. It defaults to 0.95. |
bp |
matrix containing previously simulated bootstrap series, having as rows time points, as columns variables |
ts_boot |
boolean equal to 1 if the stationary bootstrap of Politis and Romano (1994) is applied, 0 otherwise. It defaults to 1. |
Granger.inference.conditional provides bootstrap inference for 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 requires packages vars
and tseries.
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_1: percentage of non-stationary VAR models (at
least one root larger than one) estimated on bootstrapped x and z.
non_stationarity_rate_2: percentage of non-stationary VAR models (at
least one root larger than one) estimated on bootstrapped x and y and z.
delay1_mean: mean number of delays of stationary VAR models estimated on x and z.
delay2_mean: mean number of delays of stationary VAR models estimated on x and y and z.
quantile_conditional_causality_y.to.x.on.z: computed quantile of the Granger-
causality conditional spectrum from y to x on z. Differently from function
Granger.inference.unconditional, this function provides only the quantile
of the unidirectional causality from y to x.
freq_y.to.x.on.z: frequencies at which the Granger-causality conditional spectrum
from y to x condtional on z exceeds the computed threshold.
q_max_x.on.z: computed quantile of the Granger-
causality conditional spectrum from y to x on z under Bonferroni correction. Differently from function
Granger.inference.unconditional, this function provides only the quantile
of the unidirectional causality from y to x.
freq_max_y.to.x.on.z: frequencies at which the Granger-causality conditional spectrum
from y to x conditional on z exceeds the computed threshold under Bonferroni correction.
The result is returned invisibly if plot is TRUE.
Matteo Farne', Angela Montanari, [email protected]
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.
VAR and tsbootstrap.
RealGdp.rate.ts<-euro_area_indicators[,1] m3.rate.ts<-euro_area_indicators[,2] hicp.rate.ts<-euro_area_indicators[,4] inf_cond_m3.to.gdp.by.hicp_0.95<- Granger.inference.conditional(RealGdp.rate.ts,m3.rate.ts,hicp.rate.ts,nboots=10)RealGdp.rate.ts<-euro_area_indicators[,1] m3.rate.ts<-euro_area_indicators[,2] hicp.rate.ts<-euro_area_indicators[,4] inf_cond_m3.to.gdp.by.hicp_0.95<- Granger.inference.conditional(RealGdp.rate.ts,m3.rate.ts,hicp.rate.ts,nboots=10)
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).
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)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)
x |
univariate time series. |
y |
univariate time series (of the same length of |
ic.chosen |
estimation method parameter |
max.lag |
maximum number of lags |
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 |
p |
parameter |
nboots |
number of bootstrap series to be computed by function |
conf |
prescribed confidence level. It defaults to 0.95. |
bp |
matrix containing previously simulated bootstrap series, having as rows
time points, as columns variables |
ts_boot |
boolean equal to 1 if the stationary bootstrap of Politis and Romano (1994) is applied, 0 otherwise. It defaults to 1. |
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.
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.
Matteo Farne', Angela Montanari, [email protected]
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.
VAR and tsbootstrap.
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)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)
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).
Granger.unconditional(x, y, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p = 0)Granger.unconditional(x, y, ic.chosen = "SC", max.lag = min(4, length(x) - 1), plot = F, type.chosen = "none", p = 0)
x |
univariate time series. |
y |
univariate time series (of the same length of |
ic.chosen |
estimation method parameter |
max.lag |
maximum number of lags |
plot |
logical; if TRUE, it returns the plot of unconditional Granger-causality spectra on both directions. Defaults to FALSE. |
type.chosen |
parameter |
p |
parameter |
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.
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.
Matteo Farne', Angela Montanari, [email protected]
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.
VAR.
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)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)