Impulso Resposta SVAR
Felipe Andre Oliveira Freitas
2023-10-16
library("vars",quietly =T)##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericTime Series
Para seus dados use:
dados<-ts(seus_dados,start = c(1961, 1), frequency = 12)
Importando uma base de dados:
data(Canada)Modelo VAR:
model_var<- VAR(Canada, ## série temporal
p = 2, ## lag
type = "const" #const, trend or both
)
print(model_var)##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation e:
## ======================================
## Call:
## e = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const
##
## e.l1 prod.l1 rw.l1 U.l1 e.l2
## 1.637821e+00 1.672717e-01 -6.311863e-02 2.655848e-01 -4.971338e-01
## prod.l2 rw.l2 U.l2 const
## -1.016501e-01 3.844492e-03 1.326893e-01 -1.369984e+02
##
##
## Estimated coefficients for equation prod:
## =========================================
## Call:
## prod = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const
##
## e.l1 prod.l1 rw.l1 U.l1 e.l2 prod.l2
## -0.1727658 1.1504282 0.0513039 -0.4785013 0.3852589 -0.1724119
## rw.l2 U.l2 const
## -0.1188510 1.0159180 -166.7755177
##
##
## Estimated coefficients for equation rw:
## =======================================
## Call:
## rw = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const
##
## e.l1 prod.l1 rw.l1 U.l1 e.l2
## -0.268832871 -0.081065001 0.895478330 0.012130033 0.367848941
## prod.l2 rw.l2 U.l2 const
## -0.005180947 0.052676565 -0.127708256 -33.188338774
##
##
## Estimated coefficients for equation U:
## ======================================
## Call:
## U = e.l1 + prod.l1 + rw.l1 + U.l1 + e.l2 + prod.l2 + rw.l2 + U.l2 + const
##
## e.l1 prod.l1 rw.l1 U.l1 e.l2 prod.l2
## -0.58076382 -0.07811707 0.01866214 0.61893150 0.40981822 0.05211668
## rw.l2 U.l2 const
## 0.04180115 -0.07116885 149.78056487plot(model_var)
Teste de normalidade
The multivariate version of this test is computed by using the residuals that are standardized by a Choleski decomposition of the variance-covariance matrix for the centered residuals.
normality.test(model_var)## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object model_var
## Chi-squared = 5.094, df = 8, p-value = 0.7475
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object model_var
## Chi-squared = 1.7761, df = 4, p-value = 0.7769
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object model_var
## Chi-squared = 3.3179, df = 4, p-value = 0.5061Teste de Causalidade
- Opção 1: a robust HC variance-covariance matrix for the Granger test:
granger_rhc<-causality(model_var, ## modelo VAR(p)
cause = "e", ## variavel de interesse
vcov.=vcovHC(model_var),
boot=FALSE
)
granger_rhc## $Granger
##
## Granger causality H0: e do not Granger-cause prod rw U
##
## data: VAR object model_var
## F-Test = 3.3923, df1 = 6, df2 = 292, p-value = 0.002994
##
##
## $Instant
##
## H0: No instantaneous causality between: e and prod rw U
##
## data: VAR object model_var
## Chi-squared = 26.068, df = 3, p-value = 9.228e-06- Opção 2: use a wild-bootstrap procedure to for the Granger test:
granger_boot<-causality(model_var, ## modelo VAR(p)
cause = "e", ## variavel de interesse
boot=TRUE,
boot.runs=1000
)
granger_boot## $Granger
##
## Granger causality H0: e do not Granger-cause prod rw U
##
## data: VAR object model_var
## F-Test = 6.2768, boot.runs = 1000, p-value = 0.004
##
##
## $Instant
##
## H0: No instantaneous causality between: e and prod rw U
##
## data: VAR object model_var
## Chi-squared = 26.068, df = 3, p-value = 9.228e-06Modelo SVAR
Matriz diagonal
Matriz diagonal com dimensão igual ao número de variáveis do modelo, e com a diagonal principal como “NA”.
amat <- diag(4)
diag(amat) <- NA
amat## [,1] [,2] [,3] [,4]
## [1,] NA 0 0 0
## [2,] 0 NA 0 0
## [3,] 0 0 NA 0
## [4,] 0 0 0 NASVAR model - Estimation direct method
Estimating the SVAR-model with the directly minimizing the negative log-likelihood.
model_svar <-SVAR(x = model_var,
estmethod = "direct",
Amat = amat,
Bmat = NULL,
hessian = TRUE,
method= "BFGS"
)
print(model_svar)##
## SVAR Estimation Results:
## ========================
##
##
## Estimated A matrix:
## e prod rw U
## e 2.756 0.000 0.000 0.000
## prod 0.000 1.533 0.000 0.000
## rw 0.000 0.000 1.282 0.000
## U 0.000 0.000 0.000 3.576Impulse Response using SVAR
A partir do modelo SVAR estimado acima, defina as variaveis para impulso e para resposta:
- Use
boot = FALSEse nao quiser bootstrap.
impulso_resposta <- irf(model_svar, #modelo SVAR
impulse = "e", #impulse variables.
response = c("prod","rw","U"), #response variables.
n.ahead = 8, #passos a frente
ortho = FALSE, #tipo ortogonal (contemporaneo)
runs = 1000, #quantas simulacoes fazer (bootstrap)
ci= 0.95,
cumulative= TRUE #cumulative
)
print(impulso_resposta)##
## Impulse response coefficients
## $e
## prod rw U
## [1,] 0.000000000 0.00000000 0.0000000
## [2,] -0.062682030 -0.09753660 -0.2107098
## [3,] -0.001856481 -0.20863945 -0.5344652
## [4,] 0.128038245 -0.27324705 -0.9159506
## [5,] 0.272167463 -0.26034152 -1.3141711
## [6,] 0.394680480 -0.14807563 -1.6967827
## [7,] 0.474995921 0.07570693 -2.0412242
## [8,] 0.504780655 0.41395617 -2.3337765
## [9,] 0.484388446 0.86199943 -2.5680118
##
##
## Lower Band, CI= 0.95
## $e
## prod rw U
## [1,] 0.0000000 0.0000000 0.0000000
## [2,] -0.2412703 -0.2924188 -0.2880805
## [3,] -0.3780241 -0.5475483 -0.6952078
## [4,] -0.5177550 -0.7745201 -1.1601256
## [5,] -0.6626419 -0.9442921 -1.6415361
## [6,] -0.8596586 -1.0609459 -2.1206938
## [7,] -1.1426122 -1.0713947 -2.5381870
## [8,] -1.4698517 -1.0361666 -2.9407216
## [9,] -1.7906062 -0.8505542 -3.2458957
##
##
## Upper Band, CI= 0.95
## $e
## prod rw U
## [1,] 0.0000000 0.0000000 0.0000000
## [2,] 0.1242975 0.1430459 -0.1111069
## [3,] 0.4301492 0.3212939 -0.2936590
## [4,] 0.8351835 0.5731560 -0.4859137
## [5,] 1.2947294 0.9307001 -0.6706322
## [6,] 1.7125805 1.3591838 -0.7754324
## [7,] 2.1171013 1.9148577 -0.8557885
## [8,] 2.4742636 2.5262705 -0.9090738
## [9,] 2.7481305 3.1436031 -0.8986217Plot
plot(impulso_resposta)
Summary statistics
model_summary <- summary(model_svar)
model_summary ##
## SVAR Estimation Results:
## ========================
##
## Call:
## SVAR(x = model_var, estmethod = "direct", Amat = amat, Bmat = NULL,
## hessian = TRUE, method = "BFGS")
##
## Type: A-model
## Sample size: 82
## Log Likelihood: -222.436
## Method: direct
## Number of iterations: 52
## Convergence code: 0
##
## LR overidentification test:
##
## LR overidentification
##
## data: Canada
## Chi^2 = 55, df = 6, p-value = 4e-10
##
##
## Estimated A matrix:
## e prod rw U
## e 2.756 0.000 0.000 0.000
## prod 0.000 1.533 0.000 0.000
## rw 0.000 0.000 1.282 0.000
## U 0.000 0.000 0.000 3.576
##
## Estimated standard errors for A matrix:
## e prod rw U
## e 0.2152 0.0000 0.0000 0.0000
## prod 0.0000 0.1197 0.0000 0.0000
## rw 0.0000 0.0000 0.1001 0.0000
## U 0.0000 0.0000 0.0000 0.2792
##
## Estimated B matrix:
## e prod rw U
## e 1 0 0 0
## prod 0 1 0 0
## rw 0 0 1 0
## U 0 0 0 1
##
## Covariance matrix of reduced form residuals (*100):
## e prod rw U
## e 13.16 0.00 0.00 0.000
## prod 0.00 42.57 0.00 0.000
## rw 0.00 0.00 60.89 0.000
## U 0.00 0.00 0.00 7.821Variance-Covariance Matrix
The variance-covariance matrix of the reduced form residuals times
cov_mat<-model_summary$Sigma.U
cov_mat## e prod rw U
## e 13.16347 0.00000 0.00000 0.000000
## prod 0.00000 42.57107 0.00000 0.000000
## rw 0.00000 0.00000 60.88582 0.000000
## U 0.00000 0.00000 0.00000 7.820998Cholesky decomposition
Compute the Cholesky factorization of a real symmetric positive-definite square matrix.
chol_mat<-t(chol(model_summary$Sigma.U))
chol_mat## e prod rw U
## e 3.62815 0.000000 0.000000 0.000000
## prod 0.00000 6.524651 0.000000 0.000000
## rw 0.00000 0.000000 7.802937 0.000000
## U 0.00000 0.000000 0.000000 2.796605The lower triangular factor of the Cholesky decomposition, i.e., the matrix R such that R′R=x.