Granger test of predictive causality (between multivariate time series)
based on vector autoregression (VAR) model.
Its output resembles the output of the vargranger
command in Stata (but here using an F test).
Usage
granger_causality(
varmodel,
var.y = NULL,
var.x = NULL,
test = c("F", "Chisq"),
file = NULL,
check.dropped = FALSE
)Arguments
- varmodel
VAR model fitted using the
vars::VAR()function.- var.y, var.x
[Optional] Defaults to
NULL(all variables). If specified, then perform tests for specific variables. Values can be a single variable (e.g.,"X"), a vector of variables (e.g.,c("X1", "X2")), or a string containing regular expression (e.g.,"X1|X2").- test
F test and/or Wald \(\chi\)^2 test. Defaults to both:
c("F", "Chisq").- file
File name of MS Word (
.doc).- check.dropped
Check dropped variables. Defaults to
FALSE.
Details
Granger causality test (based on VAR model) examines whether the lagged values of a predictor (or predictors) help to predict an outcome when controlling for the lagged values of the outcome itself.
Granger causality does not necessarily constitute a true causal effect.
Examples
# R package "vars" should be installed
library(vars)
#> Loading required package: MASS
#>
#> Attaching package: ‘MASS’
#> The following object is masked from ‘package:dplyr’:
#>
#> select
#> Loading required package: strucchange
#> Loading required package: zoo
#>
#> Attaching package: ‘zoo’
#> The following objects are masked from ‘package:base’:
#>
#> as.Date, as.Date.numeric
#> Loading required package: sandwich
#>
#> Attaching package: ‘strucchange’
#> The following object is masked from ‘package:stringr’:
#>
#> boundary
#> Loading required package: urca
#> Loading required package: lmtest
data(Canada)
VARselect(Canada)
#> $selection
#> AIC(n) HQ(n) SC(n) FPE(n)
#> 3 2 1 3
#>
#> $criteria
#> 1 2 3 4 5
#> AIC(n) -6.191599834 -6.621627919 -6.709002047 -6.512701777 -6.30174681
#> HQ(n) -5.943189052 -6.174488511 -6.063134014 -5.668105118 -5.25842152
#> SC(n) -5.568879538 -5.500731387 -5.089929279 -4.395452772 -3.68632157
#> FPE(n) 0.002048239 0.001337721 0.001237985 0.001534875 0.00195439
#> 6 7 8 9 10
#> AIC(n) -6.194596715 -6.011720944 -6.054479536 -5.912126222 -5.867271844
#> HQ(n) -4.952542805 -4.570938409 -4.414968375 -4.073886435 -3.830303432
#> SC(n) -3.080995238 -2.399943231 -1.944525586 -1.303996035 -0.760965421
#> FPE(n) 0.002278812 0.002924622 0.003073249 0.004015164 0.004961704
#>
vm = VAR(Canada, p=3)
model_summary(vm)
#>
#> Model Summary
#>
#> ────────────────────────────────────────────────────────────────
#> e prod rw U
#> ────────────────────────────────────────────────────────────────
#> e.l1 1.753 *** -0.149 -0.472 -0.618 ***
#> (0.151) (0.289) (0.337) (0.125)
#> prod.l1 0.170 ** 1.148 *** -0.065 -0.098
#> (0.062) (0.119) (0.139) (0.052)
#> rw.l1 -0.083 0.024 0.909 *** 0.015
#> (0.053) (0.101) (0.118) (0.044)
#> U.l1 0.100 -0.658 -0.001 0.660 ***
#> (0.197) (0.379) (0.442) (0.164)
#> e.l2 -1.184 *** -0.182 0.667 0.518 **
#> (0.235) (0.451) (0.526) (0.195)
#> prod.l2 -0.106 -0.196 -0.216 0.088
#> (0.094) (0.181) (0.211) (0.078)
#> rw.l2 -0.024 -0.203 -0.146 0.070
#> (0.070) (0.133) (0.156) (0.058)
#> U.l2 -0.051 0.822 -0.301 -0.081
#> (0.245) (0.470) (0.549) (0.203)
#> e.l3 0.587 *** 0.575 -0.129 -0.030
#> (0.164) (0.315) (0.367) (0.136)
#> prod.l3 0.011 0.044 0.214 -0.011
#> (0.064) (0.122) (0.143) (0.053)
#> rw.l3 0.038 0.093 0.190 -0.039
#> (0.054) (0.103) (0.120) (0.044)
#> U.l3 0.341 0.401 0.151 0.067
#> (0.205) (0.394) (0.459) (0.170)
#> const -150.687 * -195.870 -11.669 114.367 *
#> (61.009) (116.958) (136.454) (50.598)
#> ────────────────────────────────────────────────────────────────
#> R^2 0.999 0.980 0.999 0.974
#> Adj. R^2 0.999 0.976 0.999 0.969
#> Num. obs. 81 81 81 81
#> ────────────────────────────────────────────────────────────────
#> Note. * p < .05, ** p < .01, *** p < .001.
#>
granger_causality(vm)
#>
#> Granger Causality Test (Multivariate)
#>
#> F test and Wald χ² test based on VAR(3) model:
#> ─────────────────────────────────────────────────────────
#> F df1 df2 p Chisq df p
#> ─────────────────────────────────────────────────────────
#> -----------
#> e <= prod 5.90 3 68 .001 ** 17.69 3 <.001 ***
#> e <= rw 3.29 3 68 .026 * 9.86 3 .020 *
#> e <= U 2.13 3 68 .105 6.39 3 .094 .
#> e <= ALL 3.86 9 68 <.001 *** 34.77 9 <.001 ***
#> -----------
#> prod <= e 1.90 3 68 .137 5.71 3 .127
#> prod <= rw 1.81 3 68 .154 5.42 3 .144
#> prod <= U 3.22 3 68 .028 * 9.67 3 .022 *
#> prod <= ALL 2.36 9 68 .022 * 21.21 9 .012 *
#> -----------
#> rw <= e 0.75 3 68 .527 2.25 3 .523
#> rw <= prod 1.97 3 68 .126 5.92 3 .115
#> rw <= U 0.18 3 68 .912 0.53 3 .913
#> rw <= ALL 3.58 9 68 .001 ** 32.24 9 <.001 ***
#> -----------
#> U <= e 9.53 3 68 <.001 *** 28.60 3 <.001 ***
#> U <= prod 1.58 3 68 .203 4.74 3 .192
#> U <= rw 2.19 3 68 .098 . 6.56 3 .087 .
#> U <= ALL 5.81 9 68 <.001 *** 52.26 9 <.001 ***
#> ─────────────────────────────────────────────────────────
#>