Trabalho Final - Econometria II
Fernanda Gonçalves e Giordano Bruno
2023-11-28
1- INTRODUÇÃO:
1.1 - BASES DE DADOS:
library(readxl)
setwd("C:/Users/Giordano Bruno Boff/Desktop/FGV/EESP - Ciências Econômicas/4º SEMESTRE/Econometria II/Trabalho")
#EXPORTAÇÔES:
exp = read_excel("exportacoes.xls")
colnames(exp) = c("Período", "Exportações")
exp = data.frame(exp, row.names = 1)
exp = ts(exp, start = 1995, frequency = 12)
#IMPORTAÇÕES:
imp = read_excel("importacoes.xls")
colnames(imp) = c("Período", "Importações")
imp = data.frame(imp, row.names = 1)
imp = ts(imp, start = 1995, frequency = 12)
#BALANÇA COMERCIAL:
bc = log(exp/imp)
colnames(bc) = c("Balança Comercial")
#TAXA DE CÂMBIO REAL:
tx_cambio_real = read_excel("tx_cambio_real.xls")
tx_cambio_real = tx_cambio_real[181:525,]
colnames(tx_cambio_real) = c("Período", "Taxa de Câmbio Real", "")
tx_cambio_real = data.frame(tx_cambio_real, row.names = 1)
tx_cambio_real = tx_cambio_real$Taxa.de.Câmbio.Real
tx_cambio_real = log(tx_cambio_real)
tx_cambio_real = ts(tx_cambio_real, start = 1995, frequency = 12)2 - ANÁLISE GRÁFICA
2.1 - EXPORTAÇÕES:
par(mfrow = c(2, 2))
plot(exp, type = 'line')
plot(diff(exp), type = 'line')
acf(exp)
pacf(exp)
2.2 - IMPORTAÇÕES:
par(mfrow = c(2, 2))
plot(imp, type = 'line')
plot(diff(imp), type = 'line')
acf(imp)
pacf(imp)
2.3 - BALANÇA COMERCIAL:
par(mfrow = c(2, 2))
plot(bc, type = 'line')
plot(diff(bc), type = 'line')
acf(bc)
pacf(bc)
2.5 - TAXA DE CÂMBIO REAL:
par(mfrow = c(2, 2))
plot(tx_cambio_real, type = 'line')
plot(diff(tx_cambio_real), type = 'line')
acf(tx_cambio_real)
pacf(tx_cambio_real)
3 - ESTACIONARIEDADE E RAIZ UNITÁRIA
3.1 - AUGMENTED DICKEY–FULLER TEST:
library(aTSA)
adf_bc = adf.test(bc, nlag = 21); adf_bc## Augmented Dickey-Fuller Test
## alternative: stationary
##
## Type 1: no drift no trend
## lag ADF p.value
## [1,] 0 -5.159 0.0100
## [2,] 1 -3.098 0.0100
## [3,] 2 -2.724 0.0100
## [4,] 3 -2.600 0.0100
## [5,] 4 -2.560 0.0109
## [6,] 5 -2.069 0.0396
## [7,] 6 -1.726 0.0840
## [8,] 7 -1.443 0.1631
## [9,] 8 -1.086 0.2906
## [10,] 9 -0.993 0.3240
## [11,] 10 -0.931 0.3461
## [12,] 11 -0.633 0.4526
## [13,] 12 -0.861 0.3711
## [14,] 13 -1.089 0.2898
## [15,] 14 -1.185 0.2555
## [16,] 15 -1.098 0.2865
## [17,] 16 -0.994 0.3237
## [18,] 17 -1.054 0.3020
## [19,] 18 -1.183 0.2561
## [20,] 19 -1.245 0.2339
## [21,] 20 -1.281 0.2211
## Type 2: with drift no trend
## lag ADF p.value
## [1,] 0 -6.43 0.0100
## [2,] 1 -4.10 0.0100
## [3,] 2 -3.71 0.0100
## [4,] 3 -3.56 0.0100
## [5,] 4 -3.53 0.0100
## [6,] 5 -3.01 0.0371
## [7,] 6 -2.60 0.0960
## [8,] 7 -2.26 0.2267
## [9,] 8 -1.83 0.3952
## [10,] 9 -1.72 0.4373
## [11,] 10 -1.69 0.4515
## [12,] 11 -1.44 0.5435
## [13,] 12 -1.60 0.4860
## [14,] 13 -1.77 0.4166
## [15,] 14 -1.92 0.3587
## [16,] 15 -1.82 0.4001
## [17,] 16 -1.68 0.4540
## [18,] 17 -1.79 0.4089
## [19,] 18 -1.99 0.3312
## [20,] 19 -2.10 0.2887
## [21,] 20 -2.22 0.2401
## Type 3: with drift and trend
## lag ADF p.value
## [1,] 0 -6.72 0.0100
## [2,] 1 -4.21 0.0100
## [3,] 2 -3.79 0.0197
## [4,] 3 -3.65 0.0280
## [5,] 4 -3.63 0.0302
## [6,] 5 -3.06 0.1286
## [7,] 6 -2.65 0.3012
## [8,] 7 -2.30 0.4476
## [9,] 8 -1.86 0.6361
## [10,] 9 -1.75 0.6836
## [11,] 10 -1.69 0.7086
## [12,] 11 -1.37 0.8417
## [13,] 12 -1.62 0.7384
## [14,] 13 -1.89 0.6226
## [15,] 14 -2.03 0.5617
## [16,] 15 -1.92 0.6087
## [17,] 16 -1.78 0.6682
## [18,] 17 -1.88 0.6270
## [19,] 18 -2.07 0.5471
## [20,] 19 -2.17 0.5049
## [21,] 20 -2.26 0.4679
## ----
## Note: in fact, p.value = 0.01 means p.value <= 0.01## $type1
## lag ADF p.value
## [1,] 0 -5.1587840 0.01000000
## [2,] 1 -3.0975257 0.01000000
## [3,] 2 -2.7242860 0.01000000
## [4,] 3 -2.5999320 0.01000000
## [5,] 4 -2.5595012 0.01089447
## [6,] 5 -2.0689722 0.03960906
## [7,] 6 -1.7256477 0.08399278
## [8,] 7 -1.4432171 0.16313675
## [9,] 8 -1.0863504 0.29058914
## [10,] 9 -0.9927497 0.32401796
## [11,] 10 -0.9309451 0.34609103
## [12,] 11 -0.6328490 0.45255391
## [13,] 12 -0.8608900 0.37111070
## [14,] 13 -1.0886972 0.28975099
## [15,] 14 -1.1847133 0.25545955
## [16,] 15 -1.0977115 0.28653159
## [17,] 16 -0.9936210 0.32370679
## [18,] 17 -1.0544459 0.30198360
## [19,] 18 -1.1828494 0.25612523
## [20,] 19 -1.2451048 0.23389116
## [21,] 20 -1.2810144 0.22106630
##
## $type2
## lag ADF p.value
## [1,] 0 -6.425643 0.01000000
## [2,] 1 -4.100427 0.01000000
## [3,] 2 -3.710530 0.01000000
## [4,] 3 -3.557471 0.01000000
## [5,] 4 -3.527904 0.01000000
## [6,] 5 -3.010727 0.03706855
## [7,] 6 -2.600147 0.09601545
## [8,] 7 -2.255420 0.22674607
## [9,] 8 -1.829090 0.39517621
## [10,] 9 -1.722515 0.43728074
## [11,] 10 -1.686597 0.45147082
## [12,] 11 -1.440312 0.54345834
## [13,] 12 -1.599264 0.48597350
## [14,] 13 -1.774803 0.41662339
## [15,] 14 -1.921368 0.35871988
## [16,] 15 -1.816625 0.40010089
## [17,] 16 -1.680225 0.45398822
## [18,] 17 -1.794330 0.40890896
## [19,] 18 -1.991132 0.33115824
## [20,] 19 -2.098543 0.28872340
## [21,] 20 -2.221648 0.24008839
##
## $type3
## lag ADF p.value
## [1,] 0 -6.721266 0.01000000
## [2,] 1 -4.208962 0.01000000
## [3,] 2 -3.785736 0.01972753
## [4,] 3 -3.651013 0.02799704
## [5,] 4 -3.628089 0.03018047
## [6,] 5 -3.061965 0.12864647
## [7,] 6 -2.652092 0.30122430
## [8,] 7 -2.304440 0.44760406
## [9,] 8 -1.858127 0.63606411
## [10,] 9 -1.745730 0.68357731
## [11,] 10 -1.686551 0.70859365
## [12,] 11 -1.371784 0.84165383
## [13,] 12 -1.616082 0.73838265
## [14,] 13 -1.889910 0.62262852
## [15,] 14 -2.034097 0.56167709
## [16,] 15 -1.922829 0.60871259
## [17,] 16 -1.782223 0.66815041
## [18,] 17 -1.879633 0.62697293
## [19,] 18 -2.068552 0.54711180
## [20,] 19 -2.168330 0.50493305
## [21,] 20 -2.256347 0.46785389adf_cambio = adf.test(tx_cambio_real, nlag = 6); adf_cambio## Augmented Dickey-Fuller Test
## alternative: stationary
##
## Type 1: no drift no trend
## lag ADF p.value
## [1,] 0 0.291 0.728
## [2,] 1 0.169 0.692
## [3,] 2 0.122 0.679
## [4,] 3 0.121 0.679
## [5,] 4 0.155 0.689
## [6,] 5 0.118 0.678
## Type 2: with drift no trend
## lag ADF p.value
## [1,] 0 -1.69 0.449
## [2,] 1 -2.35 0.191
## [3,] 2 -2.00 0.328
## [4,] 3 -2.06 0.304
## [5,] 4 -2.14 0.274
## [6,] 5 -2.22 0.239
## Type 3: with drift and trend
## lag ADF p.value
## [1,] 0 -1.71 0.698
## [2,] 1 -2.38 0.415
## [3,] 2 -2.06 0.549
## [4,] 3 -2.12 0.524
## [5,] 4 -2.18 0.499
## [6,] 5 -2.28 0.457
## ----
## Note: in fact, p.value = 0.01 means p.value <= 0.01## $type1
## lag ADF p.value
## [1,] 0 0.2911587 0.7276716
## [2,] 1 0.1685321 0.6923833
## [3,] 2 0.1220448 0.6790057
## [4,] 3 0.1213850 0.6788158
## [5,] 4 0.1552506 0.6885613
## [6,] 5 0.1177732 0.6777765
##
## $type2
## lag ADF p.value
## [1,] 0 -1.693404 0.4487815
## [2,] 1 -2.345135 0.1913026
## [3,] 2 -1.998813 0.3281237
## [4,] 3 -2.059974 0.3039610
## [5,] 4 -2.136098 0.2738867
## [6,] 5 -2.224931 0.2387913
##
## $type3
## lag ADF p.value
## [1,] 0 -1.710459 0.6984870
## [2,] 1 -2.381601 0.4151154
## [3,] 2 -2.063711 0.5491583
## [4,] 3 -2.123270 0.5239814
## [5,] 4 -2.182922 0.4987698
## [6,] 5 -2.281750 0.45715794 - ESPECIFICAÇÂO DO MODELO:
4.1 - CRITÉRIOS DE INFORMAÇÃO
library(vars)
VAR = cbind(bc, tx_cambio_real)
espec = VARselect(VAR); espec## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 9 2 2 9
##
## $criteria
## 1 2 3 4 5
## AIC(n) -1.074526e+01 -1.101276e+01 -1.102140e+01 -1.101931e+01 -1.100125e+01
## HQ(n) -1.071803e+01 -1.096737e+01 -1.095785e+01 -1.093761e+01 -1.090139e+01
## SC(n) -1.067695e+01 -1.089890e+01 -1.086200e+01 -1.081437e+01 -1.075077e+01
## FPE(n) 2.154732e-05 1.649005e-05 1.634828e-05 1.638270e-05 1.668166e-05
## 6 7 8 9 10
## AIC(n) -1.102300e+01 -1.104084e+01 -1.104077e+01 -1.106013e+01 -1.104785e+01
## HQ(n) -1.090498e+01 -1.090467e+01 -1.088644e+01 -1.088765e+01 -1.085721e+01
## SC(n) -1.072698e+01 -1.069928e+01 -1.065366e+01 -1.062749e+01 -1.056966e+01
## FPE(n) 1.632323e-05 1.603522e-05 1.603732e-05 1.573079e-05 1.592653e-055 - RELAÇÃO DE COINTEGRAÇÃO:
5.1 - JOHANSEN TEST:
j_test = ca.jo(VAR, type = 'trace',ecdet = 'const', K = 2, season = 12)
summary(j_test)##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , without linear trend and constant in cointegration
##
## Eigenvalues (lambda):
## [1] 0.06275245 0.02012530 0.00000000
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 1 | 6.97 7.52 9.24 12.97
## r = 0 | 29.20 17.85 19.96 24.60
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## bc.l2 tx_cambio_real.l2 constant
## bc.l2 1.0000000 1.000000 1.00000000
## tx_cambio_real.l2 -0.4329849 7.718752 -0.01499546
## constant 1.9733131 -37.993691 1.65446668
##
## Weights W:
## (This is the loading matrix)
##
## bc.l2 tx_cambio_real.l2 constant
## bc.d -0.14008268 0.002643939 1.029397e-17
## tx_cambio_real.d -0.01749186 -0.002750435 -2.834325e-186 - MODELAGEM:
6.1 - VECTOR ERROR CORRECTION MODEL (VECM):
library(tsDyn)
modelo = VECM(VAR, lag = 2, r = 1,
include = "const",
estim = 'ML')
summary(modelo)## #############
## ###Model VECM
## #############
## Full sample size: 345 End sample size: 342
## Number of variables: 2 Number of estimated slope parameters 12
## AIC -3776.654 BIC -3726.802 SSR 4.398904
## Cointegrating vector (estimated by ML):
## bc tx_cambio_real
## r1 1 -0.4779439
##
##
## ECT Intercept
## Equation bc -0.1707(0.0360)*** -0.3741(0.0796)***
## Equation tx_cambio_real -0.0114(0.0120) -0.0248(0.0265)
## bc -1 tx_cambio_real -1
## Equation bc -0.4455(0.0566)*** 0.0141(0.1630)
## Equation tx_cambio_real -0.0072(0.0188) 0.3502(0.0543)***
## bc -2 tx_cambio_real -2
## Equation bc -0.0883(0.0530). -0.1095(0.1641)
## Equation tx_cambio_real -0.0223(0.0176) -0.1423(0.0546)**7 - DIAGNÓSTICO DOS RESÍDUOS:
7.1 - ANÁLISE GRÁFICA:
par(mfrow = c(1, 2))
res = modelo$residuals
res = data.frame(res)
res_bc = res$bc
hist(res_bc)
plot(res_bc, type = 'line')
res_cambio = res$tx_cambio_real
hist(res_cambio)
plot(res_cambio, type = 'line')
7.2 - JARQUE-BERA TEST - NORMALIDADE:
library(tseries)
n_bc = jarque.bera.test(res_bc); n_bc##
## Jarque Bera Test
##
## data: res_bc
## X-squared = 146.49, df = 2, p-value < 2.2e-16n_cambio = jarque.bera.test(res_cambio); n_cambio##
## Jarque Bera Test
##
## data: res_cambio
## X-squared = 281.79, df = 2, p-value < 2.2e-167.3 - LJUNG-BOX TEST - AUTOCORRELAÇÃO:
library(tseries)
ac_bc = Box.test(res_bc, lag = 1, type = c("Ljung-Box")); ac_bc##
## Box-Ljung test
##
## data: res_bc
## X-squared = 0.0081376, df = 1, p-value = 0.9281ac_cambio = Box.test(res_cambio, lag = 1, type = c("Ljung-Box")); ac_cambio##
## Box-Ljung test
##
## data: res_cambio
## X-squared = 0.035651, df = 1, p-value = 0.85028 - CAUSALIDADE DE GRANGER:
8.1 - CURJA J:
library(lmtest)
gc_bc = grangertest(bc ~ tx_cambio_real, order = 2); gc_bc## Granger causality test
##
## Model 1: bc ~ Lags(bc, 1:2) + Lags(tx_cambio_real, 1:2)
## Model 2: bc ~ Lags(bc, 1:2)
## Res.Df Df F Pr(>F)
## 1 338
## 2 340 -2 4.6837 0.009853 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1gc_cambio = grangertest(tx_cambio_real ~ bc, order = 2); gc_cambio## Granger causality test
##
## Model 1: tx_cambio_real ~ Lags(tx_cambio_real, 1:2) + Lags(bc, 1:2)
## Model 2: tx_cambio_real ~ Lags(tx_cambio_real, 1:2)
## Res.Df Df F Pr(>F)
## 1 338
## 2 340 -2 0.857 0.4253