Exercício 6 series temp

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6º EXERCÍCIO
ECONOMETRIA DE SÉRIES TEMPORAIS
PROFESSOR: RICARDO CHAVES LIMA
ALUNA: AMANDA STEFFANY DA SILVA RAUJO 
RECIFE
2017
Exercício 6
Usando o banco de dados Canada, estime o modelo VAR com decomposição triangular (Choleski) mostrando e discutindo:
i) os parâmetros do modelo;
ii) a função de impulso-resposta;
iii) a decomposição da variância.
Note:
- usar como exemplo da estimação do VAR os arquivos var.r (programa) e gujarativardados.r (banco de dados).
gujarativardados
# M1=money supply,R=interest rate, P=price index, GDP=product
summary(gujarativardados)
#det lag langht
VARselect(gujarativar, lag.max = 8, type = "both")
#det endogeneidade
gujvar <- VAR(gujarativar, p = 3, type = "const")
causality(gujvar, cause = "M1")
causality(gujvar, cause = "R")
#ADF
adf11 <- summary(ur.df(gujarativar[, "M1"], type = "trend", lags = 3));adf11
adf12 <- summary(ur.df(gujarativar[, "R"], type = "trend", lags = 3));adf12
adf21 <- summary(ur.df(diff(gujarativar[, "M1"]), type = "drift", lags = 3));adf21
adf22 <- summary(ur.df(diff(gujarativar[, "R"]), type = "drift", lags = 3));adf22
# run VAR
gvar <- VAR(gujarativar, p = 2, type="both")
summary(gvar)
# residuals test - The H0 a joint hypothesis of the skewness being zero and the excess kurtosis being zero (normality)
ser11 <- serial.test(gvar, lags.pt = 15, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 14, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 13, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 12, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 11, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 10, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 9, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 8, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 7, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 6, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 5, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 4, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 3, type = "PT.asymptotic"); ser11$serial
ser11 <- serial.test(gvar, lags.pt = 2, type = "PT.asymptotic"); ser11$serial
norm1 <- normality.test(gvar);norm1$jb.mul
arch1 <- arch.test(gvar, lags.multi = 5);arch1$arch.mul
# residuals checking
plot(arch1, names = "M1")
plot(arch1, names = "R")
plot(stability(gvar), nc = 2); # H0 = STABILITY
# VARIANCE DECOMPOSITION
fevd(gvar, n.ahead = 15)
# IMPULSE RESPONSE FUNCTION
 # FOR R -> M1
IRFM1 = irf(gvar, impulse = "R", response = c("M1"), boot =
 TRUE, n.ahead=15,ci=0.95); IRFM1;plot(IRFM1)
 # FOR R -> R
IRFR = irf(gvar, impulse = "R", response = c("R"), boot =
 TRUE, n.ahead=15,ci=0.95); IRFR;plot(IRFR)
#####
 # FOR M1 -> R
IRFM1 = irf(gvar, impulse = "M1", response = c("R"), boot =
 TRUE, n.ahead=15,ci=0.95); IRFM1; plot(IRFM1)
 # FOR M1 -> M1
IRFR = irf(gvar, impulse = "M1", response = c("M1"), boot =
 TRUE, n.ahead=15,ci=0.95); IRFR; plot(IRFR)
CONSOLE:
> gujarativardados
 M1 R P GDP
1 22175.00 11.13333 0.77947 33480
2 22841.00 11.16667 0.80861 33670
3 23461.00 11.80000 0.82649 340096
4 23427.00 14.18333 0.84863 341844
5 23811.00 14.38333 0.86693 342776
6 23612.33 12.98330 0.88950 342264
7 24543.00 10.71667 0.91553 340716
8 25638.66 14.53333 0.93743 347780
9 25316.00 17.13333 0.96523 354836
10 25501.33 18.56667 0.98774 359352
11 25382.33 21.01666 1.01314 356152
12 24753.00 16.61665 1.03410 353636
13 25094.33 15.35000 1.05743 349568
14 25253.66 16.04999 1.07748 345284
15 24936.66 14.31667 1.09666 343028
16 25553.00 10.88333 1.11641 340292
17 26755.33 9.61667 1.12303 346072
18 27412.00 9.31667 1.13395 353860
19 28403.33 9.33333 1.14721 359544
20 28402.33 9.55000 1.16059 362304
21 28715.66 10.08333 1.17117 368280
22 28996.33 11.45000 1.17406 376768
23 28479.33 12.45000 1.17795 381016
24 28669.00 10.76667 1.18438 385396
25 29018.66 10.51667 1.18990 39024
26 29398.66 9.66667 1.20625 391580
27 30203.66 9.03333 1.21492 396384
28 31059.33 9.01667 1.21805 405308
29 30745.33 11.03333 1.22408 405680
30 30477.66 8.73333 1.22856 408116
31 31563.66 8.46667 1.23916 409160
32 32800.66 8.40000 1.25368 409616
33 33958.33 7.25000 1.27117 416484
34 35795.66 8.30000 1.28429 422916
35 35878.66 9.30000 1.29599 429980
36 36336.00 8.70000 1.31001 436264
37 36480.33 8.61667 1.32325 440592
38 37108.66 9.13333 1.33219 446680
39 38423.00 10.05000 1.35065 450328
40 38480.66 10.83333 1.36648 453516
> # M1=money supply,R=interest rate, P=price index, GDP=product
> summary(gujarativardados)
 M1 R P GDP 
 Min. :22175 Min. : 7.250 Min. :0.7795 Min. : 33480 
 1st Qu.:25214 1st Qu.: 9.258 1st Qu.:1.0068 1st Qu.:344720 
 Median :28441 Median :10.742 Median :1.1659 Median :360924 
 Mean :28872 Mean :11.511 Mean :1.1200 Mean :355491 
 3rd Qu.:31185 3rd Qu.:13.283 3rd Qu.:1.2312 3rd Qu.:408377 
 Max. :38481 Max. :21.017 Max. :1.3665 Max. :453516 
> #det lag langht
> VARselect(gujarativar, lag.max = 8, type = "both")
$selection
AIC(n) HQ(n) SC(n) FPE(n) 
 3 1 1 3 
$criteria
 1 2 3 4 5 6
AIC(n) 13.07743 13.07728 13.03905 13.26329 13.24437 13.23197
HQ(n) 13.19889 13.25947 13.28197 13.56695 13.60875 13.65709
SC(n) 13.44387 13.62693 13.77191 14.17938 14.34367 14.51449
FPE(n) 479289.52041 482269.79230 470098.15445 601118.97639 610041.24906 633180.18217
 7 8
AIC(n) 13.36761 1.355938e+01
HQ(n) 13.85346 1.410597e+01
SC(n) 14.83334 1.520834e+01
FPE(n) 778271.23513 1.040608e+06
> #det endogeneidade
> gujvar <- VAR(gujarativar, p = 3, type = "const")
> causality(gujvar, cause = "M1")
$Granger
	Granger causality H0: M1 do not Granger-cause R
data: VAR object gujvar
F-Test = 2.7255, df1 = 3, df2 = 60, p-value = 0.05198
$Instant
	H0: No instantaneous causality between: M1 and R
data: VAR object gujvar
Chi-squared = 0.00064102, df = 1, p-value = 0.9798
#p-value > 0,05 H0
> causality(gujvar, cause = "R")
$Granger
	Granger causality H0: R do not Granger-cause M1
data: VAR object gujvar
F-Test = 7.7294, df1 = 3, df2 = 60, p-value = 0.00019
$Instant
	H0: No instantaneous causality between: R and M1
data: VAR object gujvar
Chi-squared = 0.00064102, df = 1, p-value = 0.9798
#p-value > 0,05 H0
> #ADF
> adf11 <- summary(ur.df(gujarativar[, "M1"], type = "trend", lags = 3));adf11
############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 
Test regression trend 
Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
Residuals:
 Min 1Q Median 3Q Max 
-972.09 -380.19 41.78 404.35 1129.78 
Coefficients:
 Estimate Std. Error t value Pr(>|t|) 
(Intercept) 2895.57313 2015.94654 1.436 0.1613 
z.lag.1 -0.13651 0.09793 -1.394 0.1736 
tt 63.68569 37.25477 1.709 0.0977 .
z.diff.lag1 0.25318 0.19377 1.307 0.2013 
z.diff.lag2 -0.04265 0.19320 -0.221 0.8268 
z.diff.lag3 0.09738 0.19487 0.500 0.6209 
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 582.2 on 30 degrees of freedom
Multiple R-squared: 0.1579,	Adjusted R-squared: 0.0175 
F-statistic: 1.125 on 5 and 30 DF, p-value: 0.3686
Value of test-statisticis: -1.394 3.0754 1.8664 
Critical values for test statistics: 
 1pct 5pct 10pct
tau3 -4.15 -3.50 -3.18
phi2 7.02 5.13 4.31
phi3 9.31 6.73 5.61
> adf12 <- summary(ur.df(gujarativar[, "R"], type = "trend", lags = 3));adf12
############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 
Test regression trend 
Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
Residuals:
 Min 1Q Median 3Q Max 
-2.9402 -0.7891 -0.1569 0.9050 3.2822 
Coefficients:
 Estimate Std. Error t value Pr(>|t|) 
(Intercept) 5.40625 2.44767 2.209 0.0350 *
z.lag.1 -0.34894 0.14553 -2.398 0.0229 *
tt -0.06723 0.04079 -1.648 0.1097 
z.diff.lag1 0.32597 0.17622 1.850 0.0742 .
z.diff.lag2 -0.03025 0.17465 -0.173 0.8636 
z.diff.lag3 0.17375 0.17369 1.000 0.3251 
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.595 on 30 degrees of freedom
Multiple R-squared: 0.2076,	Adjusted R-squared: 0.07549 
F-statistic: 1.572 on 5 and 30 DF, p-value: 0.1982
Value of test-statistic is: -2.3978 1.9935 2.9285 
Critical values for test statistics: 
 1pct 5pct 10pct
tau3 -4.15 -3.50 -3.18
phi2 7.02 5.13 4.31
phi3 9.31 6.73 5.61
> adf21 <- summary(ur.df(diff(gujarativar[, "M1"]), type = "drift", lags = 3));adf21
############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 
Test regression drift 
Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
Residuals:
 Min 1Q Median 3Q Max 
-813.5 -488.3 -106.6 383.5 985.7 
Coefficients:
 Estimate Std. Error t value Pr(>|t|) 
(Intercept) 448.6445 153.5195 2.922 0.006545 ** 
z.lag.1 -1.0866 0.2926 -3.713 0.000835 ***
z.diff.lag1 0.3368 0.2637 1.277 0.211247 
z.diff.lag2 0.2276 0.2204 1.032 0.310164 
z.diff.lag3 0.3661 0.1773 2.065 0.047699 * 
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 577.5 on 30 degrees of freedom
Multiple R-squared: 0.4681,	Adjusted R-squared: 0.3972 
F-statistic: 6.601 on 4 and 30 DF, p-value: 0.0006186
Value of test-statistic is: -3.713 6.8978 
Critical values for test statistics: 
 1pct 5pct 10pct
tau2 -3.58 -2.93 -2.60
phi1 7.06 4.86 3.94
> adf22 <- summary(ur.df(diff(gujarativar[, "R"]), type = "drift", lags = 3));adf22
############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 
Test regression drift 
Call:
lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
Residuals:
 Min 1Q Median 3Q Max 
-3.9015 -0.7288 0.0862 0.8582 4.3815 
Coefficients:
 Estimate Std. Error t value Pr(>|t|) 
(Intercept) -0.1058 0.2919 -0.362 0.71958 
z.lag.1 -1.1609 0.3421 -3.393 0.00196 **
z.diff.lag1 0.3272 0.2899 1.129 0.26799 
z.diff.lag2 0.1090 0.2290 0.476 0.63747 
z.diff.lag3 0.1676 0.1758 0.953 0.34802 
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.718 on 30 degrees of freedom
Multiple R-squared: 0.4687,	Adjusted R-squared: 0.3979 
F-statistic: 6.618 on 4 and 30 DF, p-value: 0.0006085
Value of test-statistic is: -3.3935 5.7581 
Critical values for test statistics: 
 1pct 5pct 10pct
tau2 -3.58 -2.93 -2.60
phi1 7.06 4.86 3.94
> # run VAR
> gvar <- VAR(gujarativar, p = 2, type="both")
> summary(gvar)
VAR Estimation Results:
========================= 
Endogenous variables: R, M1 
Deterministic variables: both 
Sample size: 38 
Log Likelihood: -346.072 
Roots of the characteristic polynomial:
0.8383 0.8383 0.3928 0.3928
Call:
VAR(y = gujarativar, p = 2, type = "both")
Estimation results for equation R: 
================================== 
R = R.l1 + M1.l1 + R.l2 + M1.l2 + const + trend 
 Estimate Std. Error t value Pr(>|t|) 
R.l1 0.8558345 0.1696657 5.044 1.75e-05 ***
M1.l1 0.0011539 0.0004897 2.356 0.0248 * 
R.l2 -0.0567715 0.1662271 -0.342 0.7349 
M1.l2 -0.0006730 0.0005201 -1.294 0.2050 
const -6.7291429 4.9760262 -1.352 0.1858 
trend -0.2370593 0.0913681 -2.595 0.0142 * 
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.402 on 32 degrees of freedom
Multiple R-Squared: 0.839,	Adjusted R-squared: 0.8139 
F-statistic: 33.36 on 5 and 32 DF, p-value: 8.545e-12 
Estimation results for equation M1: 
=================================== 
M1 = R.l1 + M1.l1 + R.l2 + M1.l2 + const + trend 
 Estimate Std. Error t value Pr(>|t|) 
R.l1 -2.436e+02 5.421e+01 -4.494 8.58e-05 ***
M1.l1 1.020e+00 1.565e-01 6.519 2.43e-07 ***
R.l2 1.615e+02 5.311e+01 3.041 0.00467 ** 
M1.l2 4.328e-03 1.662e-01 0.026 0.97939 
const 9.314e+02 1.590e+03 0.586 0.56209 
trend -1.293e+01 2.919e+01 -0.443 0.66083 
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 447.9 on 32 degrees of freedom
Multiple R-Squared: 0.9917,	Adjusted R-squared: 0.9904 
F-statistic: 766.1 on 5 and 32 DF, p-value: < 2.2e-16 
Covariance matrix of residuals:
 R M1
R 1.966 -33.68
M1 -33.676 200649.25
Correlation matrix of residuals:
 R M1
R 1.00000 -0.05362
M1 -0.05362 1.00000
> # residuals test - The H0 a joint hypothesis of the skewness being zero and the excess kurtosis being zero (normality)
> ser11 <- serial.test(gvar, lags.pt = 15, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 31.426, df = 52, p-value = 0.9893
> ser11 <- serial.test(gvar, lags.pt = 14, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 28.506, df = 48, p-value = 0.9886
> ser11 <- serial.test(gvar, lags.pt = 13, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 28.063, df = 44, p-value = 0.9705
> ser11 <- serial.test(gvar, lags.pt = 12, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 25.118, df = 40, p-value = 0.9681
> ser11 <- serial.test(gvar, lags.pt = 11, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 22.243, df = 36, p-value = 0.9648
> ser11 <- serial.test(gvar, lags.pt = 10, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 21.209, df = 32, p-value = 0.927
> ser11 <- serial.test(gvar, lags.pt = 9, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 19.396, df = 28, p-value = 0.8855
> ser11 <- serial.test(gvar, lags.pt = 8, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 18.38, df = 24, p-value = 0.7842
> ser11 <- serial.test(gvar, lags.pt = 7, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 15.247, df = 20, p-value = 0.7621
> ser11 <- serial.test(gvar, lags.pt = 6, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 12.703, df = 16, p-value = 0.6944
> ser11 <- serial.test(gvar, lags.pt = 5, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data:Residuals of VAR object gvar
Chi-squared = 12.033, df = 12, p-value = 0.443
> ser11 <- serial.test(gvar, lags.pt = 4, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 10.358, df = 8, p-value = 0.2408
> ser11 <- serial.test(gvar, lags.pt = 3, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 4.8489, df = 4, p-value = 0.3032
> ser11 <- serial.test(gvar, lags.pt = 2, type = "PT.asymptotic"); ser11$serial
	Portmanteau Test (asymptotic)
data: Residuals of VAR object gvar
Chi-squared = 3.1567, df = 0, p-value < 2.2e-16
> norm1 <- normality.test(gvar);norm1$jb.mul
$JB
	JB-Test (multivariate)
data: Residuals of VAR object gvar
Chi-squared = 0.4718, df = 4, p-value = 0.9762
$Skewness
	Skewness only (multivariate)
data: Residuals of VAR object gvar
Chi-squared = 0.21039, df = 2, p-value = 0.9001
$Kurtosis
	Kurtosis only (multivariate)
data: Residuals of VAR object gvar
Chi-squared = 0.26141, df = 2, p-value = 0.8775
> arch1 <- arch.test(gvar, lags.multi = 5);arch1$arch.mul
	ARCH (multivariate)
data: Residuals of VAR object gvar
Chi-squared = 49.204, df = 45, p-value = 0.3086
> # residuals checking
> plot(arch1, names = "M1")
> plot(arch1, names = "R")
> plot(stability(gvar), nc = 2); # H0 = STABILITY
> # VARIANCE DECOMPOSITION
> fevd(gvar, n.ahead = 15)
$R
 R M1
 [1,] 1.0000000 0.0000000
 [2,] 0.9261224 0.0738776
 [3,] 0.8352334 0.1647666
 [4,] 0.7659168 0.2340832
 [5,] 0.7147681 0.2852319
 [6,] 0.6769925 0.3230075
 [7,] 0.6514082 0.3485918
 [8,] 0.6360163 0.3639837
 [9,] 0.6278636 0.3721364
[10,] 0.6243328 0.3756672
[11,] 0.6235493 0.3764507
[12,] 0.6242637 0.3757363
[13,] 0.6256775 0.3743225
[14,] 0.6273080 0.3726920
[15,] 0.6288850 0.3711150
$M1
 R M1
 [1,] 0.002875338 0.9971247
 [2,] 0.247926550 0.7520735
 [3,] 0.380015555 0.6199844
 [4,] 0.437689936 0.5623101
 [5,] 0.469875016 0.5301250
 [6,] 0.492950195 0.5070498
 [7,] 0.510553682 0.4894463
 [8,] 0.523726400 0.4762736
 [9,] 0.533426085 0.4665739
[10,] 0.540510804 0.4594892
[11,] 0.545628095 0.4543719
[12,] 0.549262149 0.4507379
[13,] 0.551789602 0.4482104
[14,] 0.553506435 0.4464936
[15,] 0.554642007 0.4453580
> # IMPULSE RESPONSE FUNCTION
> # FOR R -> M1
> IRFM1 = irf(gvar, impulse = "R", response = c("M1"), boot =
+ TRUE, n.ahead=15,ci=0.95); IRFM1;plot(IRFM1)
Impulse response coefficients
$R
 M1
 [1,] -24.01946
 [2,] -366.07288
 [3,] -432.65608
 [4,] -379.64172
 [5,] -335.62101
 [6,] -306.84908
 [7,] -277.32335
 [8,] -244.59288
 [9,] -211.95348
[10,] -181.39309
[11,] -153.40818
[12,] -128.13053
[13,] -105.65505
[14,] -85.98609
[15,] -69.01670
[16,] -54.56514
Lower Band, CI= 0.95 
$R
 M1
 [1,] -129.4027
 [2,] -505.2053
 [3,] -597.9857
 [4,] -546.4038
 [5,] -507.9629
 [6,] -489.0544
 [7,] -455.4713
 [8,] -356.9681
 [9,] -301.1448
[10,] -256.6318
[11,] -218.5784
[12,] -183.8940
[13,] -150.4891
[14,] -134.5395
[15,] -123.4583
[16,] -113.2513
Upper Band, CI= 0.95 
$R
 M1
 [1,] 104.156459
 [2,] -98.327407
 [3,] -125.585207
 [4,] -47.692715
 [5,] -8.646694
 [6,] 70.303894
 [7,] 71.588619
 [8,] 59.041029
 [9,] 62.896604
[10,] 118.235047
[11,] 139.728198
[12,] 133.944820
[13,] 136.286059
[14,] 143.793237
[15,] 102.908433
[16,] 73.836164
> # FOR R -> R
> IRFR = irf(gvar, impulse = "R", response = c("R"), boot =
+ TRUE, n.ahead=15,ci=0.95); IRFR;plot(IRFR)
Impulse response coefficients
$R
 R
 [1,] 1.40203658
 [2,] 1.17219409
 [3,] 0.51734455
 [4,] 0.12330862
 [5,] -0.07075992
 [6,] -0.19936004
 [7,] -0.29482626
 [8,] -0.35452030
 [9,] -0.38228951
[10,] -0.38702897
[11,] -0.37620898
[12,] -0.35495296
[13,] -0.32703957
[14,] -0.29543269
[15,] -0.26239553
[16,] -0.22957043
Lower Band, CI= 0.95 
$R
 R
 [1,] 1.0093853
 [2,] 0.5046052
 [3,] -0.1930699
 [4,] -0.5855353
 [5,] -0.7391841
 [6,] -0.6386010
 [7,] -0.6885408
 [8,] -0.7821425
 [9,] -0.7606070
[10,] -0.6869465
[11,] -0.6570140
[12,] -0.6090838
[13,] -0.5343836
[14,] -0.4928135
[15,] -0.4450044
[16,] -0.3943514
Upper Band, CI= 0.95 
$R
 R
 [1,] 1.66504821
 [2,] 1.60452327
 [3,] 1.03423652
 [4,] 0.54452930
 [5,] 0.16586024
 [6,] 0.08795477
 [7,] 0.07413740
 [8,] 0.06692587
 [9,] 0.10940924
[10,] 0.09354612
[11,] 0.07319918
[12,] 0.04176290
[13,] 0.03707668
[14,] 0.09075407
[15,] 0.11875789
[16,] 0.13119084
> #####
> # FOR M1 -> R
> IRFM1 = irf(gvar, impulse = "M1", response = c("R"), boot =
+ TRUE, n.ahead=15,ci=0.95); IRFM1; plot(IRFM1)
Impulse response coefficients
$M1
 R
 [1,] 0.0000000
 [2,] 0.5161535
 [3,] 0.6672451
 [4,] 0.6289079
 [5,] 0.5834877
 [6,] 0.5496872
 [7,] 0.5091896
 [8,] 0.4597863
 [9,] 0.4072263
[10,] 0.3555206
[11,] 0.3063502
[12,] 0.2605934
[13,] 0.2188696
[14,] 0.1815251
[15,] 0.1486357
[16,] 0.1200812
Lower Band, CI= 0.95 
$M1
 R
 [1,] 0.00000000
 [2,] 0.09908932
 [3,] 0.14560273
 [4,] -0.02241492
 [5,] -0.07462619
 [6,] -0.06731903
 [7,] -0.07782605
 [8,] -0.10535767
 [9,] -0.15670871
[10,] -0.25715848
[11,] -0.28562277
[12,] -0.25186633
[13,] -0.24358790
[14,] -0.25354556
[15,] -0.28601416
[16,] -0.26641785
Upper Band, CI= 0.95 
$M1
 R
 [1,] 0.0000000
 [2,] 0.8230671
 [3,] 1.0917137
 [4,] 1.0352449
 [5,] 0.9137671
 [6,] 0.7963934
 [7,] 0.7408441
 [8,] 0.6566320
 [9,] 0.5171422
[10,] 0.4305844
[11,] 0.3654430
[12,] 0.2751083
[13,] 0.2226122
[14,] 0.1969125
[15,] 0.1749518
[16,] 0.1552076
> # FOR M1 -> M1
> IRFR = irf(gvar, impulse = "M1", response = c("M1"), boot =
+ TRUE, n.ahead=15,ci=0.95); IRFR; plot(IRFR)
Impulse response coefficients
$M1
 M1
 [1,] 447.29444
 [2,] 456.27712
 [3,] 341.62805
 [4,] 271.27157
 [5,] 232.74929
 [6,] 198.02242
 [7,] 163.33012
 [8,] 132.19782
 [9,] 105.78512
[10,] 83.53290
[11,] 64.82713
[12,] 49.27739
[13,] 36.54021
[14,] 26.25457
[15,] 18.06635
[16,] 11.65018
Lower Band, CI= 0.95 
$M1
 M1
 [1,] 308.38706
 [2,] 204.58111
 [3,] 24.05020
 [4,] -60.50809
 [5,] -98.90887
 [6,] -136.42739
 [7,] -133.63199
 [8,] -149.33572
 [9,] -141.31264
[10,] -125.80934
[11,] -133.98960
[12,] -138.56635
[13,] -143.08566
[14,] -145.82633
[15,] -140.80743
[16,] -130.18343
Upper Band, CI= 0.95 
$M1
 M1
 [1,] 485.23980
 [2,] 491.31200
 [3,] 412.04729
 [4,] 332.71650
 [5,] 308.64750
 [6,] 267.56917
 [7,] 205.83740
 [8,] 164.98744
 [9,] 151.63159
[10,] 148.00966
[11,] 141.53521
[12,] 131.97439
[13,] 121.47866
[14,] 111.81754
[15,] 103.50382
[16,] 96.30831
P-value > 0,05 H0
P-value <0,05 H1
O ideal é o modelo todo no H0, pois os resíduos são não-autocorrelacionados. 
Decomposição da variância em percentual mostra o impacto em uma variável provocado por um choque em outra variável.
 
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