rm(list=ls())
if (!require("pacman")) install.packages("pacman")
## Carregando pacotes exigidos: pacman
## Warning: package 'pacman' was built under R version 4.2.3
library(pacman)
carregar_pacotes <- function() {
pacman::p_load(
ggplot2,
gridExtra,
ipeadatar,
tseries,
dplyr,
forecast,
lmtest,
FinTS,
tidyverse,
lubridate,
urca,
vars
)
}
carregar_pacotes()
## Importação dos dados
seriesbr <- ipeadatar::available_series("br")
preço_grão_inter <- ipeadata("IFS_SOJAGP")
exp_grão_quant <- ipeadata("HIST_XSOJAQ")
preço_saca_br <- ipeadata("DERAL12_PRSO12")
tax_câmbio <- ipeadata("BM_ERC")
## Transformando as periodicidades das séries
preço_saca_br <- preço_saca_br %>%
mutate(date = format(date, "%Y")) %>%
group_by(date) %>%
summarize(cot_br = mean(value))
preço_grão_inter <- preço_grão_inter %>%
mutate(date = format(date, "%Y")) %>%
group_by(date)
preço_grão_inter <- preço_grão_inter %>%
summarize(cot_inter = value*0.06)
exp_grão_quant <- exp_grão_quant %>%
mutate(date = format(date, "%Y")) %>%
group_by(date)
exp_grão_quant <- exp_grão_quant %>%
rename(exp_quant = value)
tax_câmbio <- tax_câmbio %>%
mutate(date = format(date, "%Y")) %>%
group_by(date)
tax_câmbio <- tax_câmbio %>%
rename(tx_câmbio = value)
## Filtrando os períodos
preço_saca_br <- preço_saca_br %>%
filter(date>=1990) %>%
filter(date<=2023)
preço_grão_inter <- preço_grão_inter %>%
filter(date>=1990) %>%
filter(date<=2023)
exp_grão_quant <- exp_grão_quant %>%
filter(date>=1990) %>%
filter(date<=2023)
tax_câmbio <- tax_câmbio %>%
filter(date>=1990) %>%
filter(date<=2023)
## Filtrando as variáveis
preço_grão_inter_subset <- preço_grão_inter[, c("cot_inter")]
exp_grão_quant_subset <- exp_grão_quant[, c("exp_quant", "date")]
tax_câmbio_subset <- tax_câmbio[, c("tx_câmbio")]
preço_saca_br <- preço_saca_br[, c("cot_br")]
## Construindo a base de dados
dados <-cbind(tax_câmbio_subset, preço_grão_inter_subset, preço_saca_br, exp_grão_quant_subset)
view(dados)
## Plotando variação da cotação doméstica contra cotação internacional (ambos em reais por saca por meio da taxa de câmbio)
cot_inter_reais <- dados$cot_inter*dados$tx_câmbio
dados_gráfico <- cbind(dados, cot_inter_reais)
plot_inter <- ggplot(dados_gráfico, aes(date, cot_inter_reais)) + geom_point()
plot_br <- ggplot(dados_gráfico, aes(date, cot_br)) + geom_point()
grid.arrange(plot_br, plot_inter, ncol=2, nrow=2)
## Transformação das variáveis em log e declaração de séries temporais
lpgi <- as.vector(log(dados$cot_inter))
legq <- as.vector(log(dados$exp_quant))
lpsb <- as.vector(log(dados$cot_br))
ltxc <- as.vector(log(dados$tx_câmbio))
lpgi <- ts(lpgi, start = c(1990), frequency = 1)
legq <- ts(legq, start = c(1990), frequency = 1)
lpsb <- ts(lpsb, start = c(1990), frequency = 1)
ltxc <- ts(ltxc, start = c(1990), frequency = 1)
## TESTE ADF: Adotando um alfa = 5%
#ADF lpgi
#M3
M3_lpgi<-ur.df(lpgi, type = "trend", selectlags = c("BIC"))
summary(M3_lpgi) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária (M2)
##
## ###############################################
## # 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
## -0.302864 -0.093277 -0.002279 0.098564 0.260382
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.905341 0.306256 2.956 0.00626 **
## z.lag.1 -0.374983 0.126450 -2.965 0.00612 **
## tt 0.011160 0.004659 2.396 0.02352 *
## z.diff.lag 0.402181 0.175068 2.297 0.02929 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1535 on 28 degrees of freedom
## Multiple R-squared: 0.2742, Adjusted R-squared: 0.1965
## F-statistic: 3.526 on 3 and 28 DF, p-value: 0.02764
##
##
## Value of test-statistic is: -2.9655 3.1555 4.4107
##
## 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
#M2
M2_lpgi<-ur.df(lpgi, type = "drift", selectlags = c("BIC"))
summary(M2_lpgi) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária (M1)
##
## ###############################################
## # 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
## -0.29885 -0.08180 -0.01275 0.08265 0.34846
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.42690 0.25042 1.705 0.0989 .
## z.lag.1 -0.14100 0.08662 -1.628 0.1144
## z.diff.lag 0.31154 0.18437 1.690 0.1018
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1656 on 29 degrees of freedom
## Multiple R-squared: 0.1255, Adjusted R-squared: 0.06516
## F-statistic: 2.08 on 2 and 29 DF, p-value: 0.1431
##
##
## Value of test-statistic is: -1.6278 1.6022
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1 7.06 4.86 3.94
#M1
M1_lpgi<-ur.df(lpgi, type = "none", selectlags = c("BIC"))
summary(M1_lpgi) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária (M1)
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27512 -0.08707 0.00365 0.09211 0.36910
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 0.005617 0.010606 0.530 0.600
## z.diff.lag 0.216769 0.181283 1.196 0.241
##
## Residual standard error: 0.1708 on 30 degrees of freedom
## Multiple R-squared: 0.06467, Adjusted R-squared: 0.002312
## F-statistic: 1.037 on 2 and 30 DF, p-value: 0.3669
##
##
## Value of test-statistic is: 0.5297
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61
#ADF legq
#M3
M3_legq<-ur.df(legq, type = "trend", selectlags = c("BIC"))
summary(M3_legq) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária (M2)
##
## ###############################################
## # 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
## -0.57387 -0.07054 0.01538 0.10316 0.39524
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.30254 2.56768 2.844 0.00823 **
## z.lag.1 -0.47711 0.17334 -2.753 0.01026 *
## tt 0.04861 0.01981 2.454 0.02059 *
## z.diff.lag -0.04670 0.15693 -0.298 0.76821
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1861 on 28 degrees of freedom
## Multiple R-squared: 0.3442, Adjusted R-squared: 0.2739
## F-statistic: 4.898 on 3 and 28 DF, p-value: 0.00734
##
##
## Value of test-statistic is: -2.7526 9.2674 4.7771
##
## 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
#M2
M2_legq<-ur.df(legq, type = "drift", selectlags = c("BIC"))
summary(M2_legq) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária (M1)
##
## ###############################################
## # 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
## -0.59431 -0.10039 0.00986 0.10068 0.59101
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.13336 0.56856 1.993 0.0557 .
## z.lag.1 -0.05862 0.03380 -1.735 0.0934 .
## z.diff.lag -0.26724 0.13936 -1.918 0.0651 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2016 on 29 degrees of freedom
## Multiple R-squared: 0.2031, Adjusted R-squared: 0.1481
## F-statistic: 3.695 on 2 and 29 DF, p-value: 0.0372
##
##
## Value of test-statistic is: -1.7345 9.2809
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1 7.06 4.86 3.94
#M1
M1_legq<-ur.df(legq, type = "none", selectlags = c("BIC"))
summary(M1_legq) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária (M2)
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.4979 -0.1193 -0.0069 0.1116 0.7096
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 0.008599 0.002360 3.643 0.00101 **
## z.diff.lag -0.287511 0.145714 -1.973 0.05776 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2113 on 30 degrees of freedom
## Multiple R-squared: 0.316, Adjusted R-squared: 0.2704
## F-statistic: 6.931 on 2 and 30 DF, p-value: 0.003354
##
##
## Value of test-statistic is: 3.6432
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61
#ADF lpsb
#M3
M3_lpsb<-ur.df(lpsb, type = "trend", selectlags = c("BIC"))
summary(M3_lpsb) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -0.88193 -0.14589 0.02437 0.13878 0.96321
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.611100 0.170761 3.579 0.00128 **
## z.lag.1 -0.281425 0.041386 -6.800 2.19e-07 ***
## tt 0.023800 0.009034 2.634 0.01358 *
## z.diff.lag 0.343889 0.096300 3.571 0.00131 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3268 on 28 degrees of freedom
## Multiple R-squared: 0.8613, Adjusted R-squared: 0.8465
## F-statistic: 57.98 on 3 and 28 DF, p-value: 3.928e-12
##
##
## Value of test-statistic is: -6.8 16.2166 24.1848
##
## 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
#M2
M2_lpsb<-ur.df(lpsb, type = "drift", selectlags = c("BIC"))
summary(M2_lpsb) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -1.0752 -0.1086 -0.0243 0.1511 0.9304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8565 0.1571 5.453 7.21e-06 ***
## z.lag.1 -0.2199 0.0375 -5.864 2.31e-06 ***
## z.diff.lag 0.3253 0.1054 3.086 0.00443 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3587 on 29 degrees of freedom
## Multiple R-squared: 0.827, Adjusted R-squared: 0.815
## F-statistic: 69.3 on 2 and 29 DF, p-value: 8.97e-12
##
##
## Value of test-statistic is: -5.864 17.3092
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1 7.06 4.86 3.94
#M1
M1_lpsb<-ur.df(lpsb, type = "none", selectlags = c("BIC"))
summary(M1_lpsb) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.90644 -0.03251 0.18689 0.37081 0.95427
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.03732 0.02363 -1.580 0.125
## z.diff.lag 0.76908 0.09377 8.202 3.72e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5019 on 30 degrees of freedom
## Multiple R-squared: 0.7046, Adjusted R-squared: 0.6849
## F-statistic: 35.78 on 2 and 30 DF, p-value: 1.138e-08
##
##
## Value of test-statistic is: -1.5796
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61
#ADF ltxc
#M3
M3_ltxc<-ur.df(ltxc, type = "trend", selectlags = c("BIC"))
summary(M3_ltxc) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -0.89884 -0.08791 -0.02490 0.09449 0.95679
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.001385 0.158835 -0.009 0.993106
## z.lag.1 -0.263185 0.038898 -6.766 2.39e-07 ***
## tt 0.012959 0.007899 1.641 0.112072
## z.diff.lag 0.361302 0.095378 3.788 0.000739 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3115 on 28 degrees of freedom
## Multiple R-squared: 0.8706, Adjusted R-squared: 0.8568
## F-statistic: 62.81 on 3 and 28 DF, p-value: 1.496e-12
##
##
## Value of test-statistic is: -6.766 15.7797 23.5489
##
## 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
#M2
M2_ltxc<-ur.df(ltxc, type = "drift", selectlags = c("BIC"))
summary(M2_ltxc) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -0.96051 -0.12902 -0.00717 0.11906 0.95768
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.23427 0.06974 3.359 0.00220 **
## z.lag.1 -0.23778 0.03671 -6.478 4.34e-07 ***
## z.diff.lag 0.32857 0.09595 3.424 0.00186 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3205 on 29 degrees of freedom
## Multiple R-squared: 0.8582, Adjusted R-squared: 0.8484
## F-statistic: 87.75 on 2 and 29 DF, p-value: 5.011e-13
##
##
## Value of test-statistic is: -6.4776 21.0934
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1 7.06 4.86 3.94
#M1
M1_ltxc<-ur.df(ltxc, type = "none", selectlags = c("BIC"))
summary(M1_ltxc) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.26028 0.07753 0.14255 0.27737 0.82682
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.18194 0.03792 -4.797 4.13e-05 ***
## z.diff.lag 0.51578 0.09051 5.699 3.24e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3714 on 30 degrees of freedom
## Multiple R-squared: 0.8304, Adjusted R-squared: 0.8191
## F-statistic: 73.47 on 2 and 30 DF, p-value: 2.751e-12
##
##
## Value of test-statistic is: -4.7974
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61
## Testes ADF com uma diferença
#ADF lpgi *com diferença*
#M3
M3_lpgi_d<-ur.df(diff(lpgi), type = "trend", selectlags = c("BIC"))
summary(M3_lpgi_d) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -0.296322 -0.092914 0.002373 0.104299 0.275749
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.012846 0.060483 0.212 0.83340
## z.lag.1 -1.171093 0.213112 -5.495 8.08e-06 ***
## tt 0.001137 0.003171 0.359 0.72265
## z.diff.lag 0.491534 0.170920 2.876 0.00777 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1568 on 27 degrees of freedom
## Multiple R-squared: 0.5327, Adjusted R-squared: 0.4808
## F-statistic: 10.26 on 3 and 27 DF, p-value: 0.0001107
##
##
## Value of test-statistic is: -5.4952 10.0965 15.1406
##
## 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
#M2
M2_lpgi_d<-ur.df(diff(lpgi), type = "drift", selectlags = c("BIC"))
summary(M2_lpgi_d) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -0.287359 -0.096071 0.006476 0.103695 0.290685
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.03191 0.02841 1.123 0.27089
## z.lag.1 -1.16210 0.20831 -5.579 5.72e-06 ***
## z.diff.lag 0.48719 0.16782 2.903 0.00713 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1543 on 28 degrees of freedom
## Multiple R-squared: 0.5305, Adjusted R-squared: 0.497
## F-statistic: 15.82 on 2 and 28 DF, p-value: 2.527e-05
##
##
## Value of test-statistic is: -5.5786 15.5648
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1 7.06 4.86 3.94
#M1
M1_lpgi_d<-ur.df(diff(lpgi), type = "none", selectlags = c("BIC"))
summary(M1_lpgi_d) #Valor do teste < Valor crítico, portanto, rejeita-se a hipótese nula, não há raiz unitária e a série é estacionária
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.25105 -0.06759 0.03070 0.13656 0.32163
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -1.1112 0.2042 -5.441 7.46e-06 ***
## z.diff.lag 0.4654 0.1674 2.780 0.00945 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.155 on 29 degrees of freedom
## Multiple R-squared: 0.5095, Adjusted R-squared: 0.4756
## F-statistic: 15.06 on 2 and 29 DF, p-value: 3.271e-05
##
##
## Value of test-statistic is: -5.4407
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61
#ADF legq *com diferença*
#M3
M3_legq_d<-ur.df(diff(legq), type = "trend", selectlags = c("BIC"))
summary(M3_legq_d) #Valor do teste < Valor crítico, portanto, rejeita-se a hipótese nula, não há raiz unitária e a série é estacionária
##
## ###############################################
## # 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
## -0.54630 -0.11814 -0.00415 0.12790 0.48888
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.239398 0.087028 2.751 0.0105 *
## z.lag.1 -1.618745 0.261505 -6.190 1.28e-06 ***
## tt -0.003870 0.004007 -0.966 0.3428
## z.diff.lag 0.310275 0.142368 2.179 0.0382 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1925 on 27 degrees of freedom
## Multiple R-squared: 0.6782, Adjusted R-squared: 0.6424
## F-statistic: 18.97 on 3 and 27 DF, p-value: 8.032e-07
##
##
## Value of test-statistic is: -6.1901 12.8391 19.2519
##
## 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
#M2
M2_legq_d<-ur.df(diff(legq), type = "drift", selectlags = c("BIC"))
summary(M2_legq_d) #Valor do teste < Valor crítico, portanto, rejeita-se a hipótese nula, não há raiz unitária e a série é estacionária
##
## ###############################################
## # 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
## -0.50214 -0.13290 -0.01961 0.10611 0.54108
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.16716 0.04442 3.763 0.00079 ***
## z.lag.1 -1.56218 0.25455 -6.137 1.27e-06 ***
## z.diff.lag 0.29853 0.14168 2.107 0.04419 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1922 on 28 degrees of freedom
## Multiple R-squared: 0.6671, Adjusted R-squared: 0.6433
## F-statistic: 28.05 on 2 and 28 DF, p-value: 2.056e-07
##
##
## Value of test-statistic is: -6.1369 18.8378
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1 7.06 4.86 3.94
#M1
M1_legq_d<-ur.df(diff(legq), type = "none", selectlags = c("BIC"))
summary(M1_legq_d) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45284 -0.00311 0.09461 0.20679 0.80130
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.9606 0.2389 -4.021 0.000377 ***
## z.diff.lag 0.0503 0.1512 0.333 0.741758
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2318 on 29 degrees of freedom
## Multiple R-squared: 0.4993, Adjusted R-squared: 0.4648
## F-statistic: 14.46 on 2 and 29 DF, p-value: 4.402e-05
##
##
## Value of test-statistic is: -4.0214
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61
#ADF lpsb *com diferença*
#M3
M3_lpsb_d<-ur.df(diff(lpsb), type = "trend", selectlags = c("BIC"))
summary(M3_lpsb_d)
##
## ###############################################
## # 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
## -1.68176 -0.21951 0.04139 0.14825 1.17516
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.23960 0.25364 0.945 0.35321
## z.lag.1 -0.39629 0.13333 -2.972 0.00615 **
## tt -0.01005 0.01194 -0.842 0.40714
## z.diff.lag 0.17715 0.17474 1.014 0.31966
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.492 on 27 degrees of freedom
## Multiple R-squared: 0.2655, Adjusted R-squared: 0.1839
## F-statistic: 3.254 on 3 and 27 DF, p-value: 0.03705
##
##
## Value of test-statistic is: -2.9722 3.5948 4.8811
##
## 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
#M2
M2_lpsb_d<-ur.df(diff(lpsb), type = "drift", selectlags = c("BIC"))
summary(M2_lpsb_d) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -1.71197 -0.21846 0.00865 0.17459 1.22679
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.04302 0.09865 0.436 0.66611
## z.lag.1 -0.33416 0.11048 -3.025 0.00529 **
## z.diff.lag 0.13384 0.16613 0.806 0.42722
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4894 on 28 degrees of freedom
## Multiple R-squared: 0.2463, Adjusted R-squared: 0.1924
## F-statistic: 4.574 on 2 and 28 DF, p-value: 0.0191
##
##
## Value of test-statistic is: -3.0246 5.0905
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1 7.06 4.86 3.94
#M1
M1_lpsb_d<-ur.df(diff(lpsb), type = "none", selectlags = c("BIC"))
summary(M1_lpsb_d) #Valor do teste < Valor crítico, portanto, rejeita-se a hipótese nula, não há raiz unitária e a série é estacionária
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.73335 -0.17772 0.04662 0.21899 1.22659
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.31272 0.09754 -3.206 0.00327 **
## z.diff.lag 0.11908 0.16035 0.743 0.46370
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4826 on 29 degrees of freedom
## Multiple R-squared: 0.2619, Adjusted R-squared: 0.211
## F-statistic: 5.144 on 2 and 29 DF, p-value: 0.01224
##
##
## Value of test-statistic is: -3.2059
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61
#ADF ltxc *com diferença*
#M3
M3_ltxc_d<-ur.df(diff(ltxc), type = "trend", selectlags = c("BIC"))
summary(M3_ltxc_d) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -1.66687 -0.12118 -0.03632 0.17996 1.15244
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.20866 0.23960 0.871 0.39150
## z.lag.1 -0.37987 0.12752 -2.979 0.00605 **
## tt -0.00859 0.01140 -0.754 0.45755
## z.diff.lag 0.22296 0.17150 1.300 0.20457
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4623 on 27 degrees of freedom
## Multiple R-squared: 0.2774, Adjusted R-squared: 0.1971
## F-statistic: 3.455 on 3 and 27 DF, p-value: 0.03026
##
##
## Value of test-statistic is: -2.9789 3.6803 5.1145
##
## 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
#M2
M2_ltxc_d<-ur.df(diff(ltxc), type = "drift", selectlags = c("BIC"))
summary(M2_ltxc_d) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # 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
## -1.69854 -0.10243 -0.02721 0.15547 1.19263
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.04181 0.09096 0.460 0.64931
## z.lag.1 -0.32477 0.10368 -3.132 0.00404 **
## z.diff.lag 0.18553 0.16288 1.139 0.26434
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4588 on 28 degrees of freedom
## Multiple R-squared: 0.2622, Adjusted R-squared: 0.2095
## F-statistic: 4.975 on 2 and 28 DF, p-value: 0.01416
##
##
## Value of test-statistic is: -3.1325 5.3184
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1 7.06 4.86 3.94
#M1
M1_ltxc_d<-ur.df(diff(ltxc), type = "none", selectlags = c("BIC"))
summary(M1_ltxc_d) #Valor do teste > Valor crítico, portanto, não rejeita-se a hipótese nula, há raiz unitária e a série é não-estacionária
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.71506 -0.06468 0.01680 0.19820 1.19662
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.30519 0.09322 -3.274 0.00275 **
## z.diff.lag 0.17044 0.15736 1.083 0.28766
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4525 on 29 degrees of freedom
## Multiple R-squared: 0.2741, Adjusted R-squared: 0.224
## F-statistic: 5.475 on 2 and 29 DF, p-value: 0.009608
##
##
## Value of test-statistic is: -3.2737
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61
## Diferenciando variáveis e agregando em dataframes
dlpgi <- diff(lpgi)
dlegq <- diff(legq)
dlpsb <- diff(lpsb)
dltxc <- diff(ltxc)
dados_ts <- ts(as.data.frame(cbind(ltxc, lpgi, lpsb, legq),
start = c(1990, frequency = 1)))
ddados_ts <- ts(as.data.frame(cbind(dltxc, dlpgi, dlpsb, dlegq),
start = c(1990), frequency = 1))
## TESTE DE COINTEGRAÇÃO: utilizando critério de Schwarz (4 defasagens)
#Ordem do teste traço
VARselect((dados_ts), lag.max = 4, type="const", season = NULL, exogen = NULL)
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 3 3 3 3
##
## $criteria
## 1 2 3 4
## AIC(n) -1.565266e+01 -1.645785e+01 -1.799217e+01 -1.787162e+01
## HQ(n) -1.535382e+01 -1.591995e+01 -1.721519e+01 -1.685557e+01
## SC(n) -1.471852e+01 -1.477642e+01 -1.556343e+01 -1.469557e+01
## FPE(n) 1.612839e-07 7.682802e-08 1.961659e-08 3.178858e-08
#Traço transitório
jotest_traco_tr <- ca.jo((dados_ts), type="trace", K=3, ecdet = "const", spec="transitory",
season = NULL, dumvar = NULL) # Há até três níveis de cointegração
summary(jotest_traco_tr)
##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , without linear trend and constant in cointegration
##
## Eigenvalues (lambda):
## [1] 9.359966e-01 7.015766e-01 3.490419e-01 2.317578e-01 2.070216e-16
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 3 | 8.17 7.52 9.24 12.97
## r <= 2 | 21.48 17.85 19.96 24.60
## r <= 1 | 58.97 32.00 34.91 41.07
## r = 0 | 144.18 49.65 53.12 60.16
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## ltxc.l1 lpgi.l1 lpsb.l1 legq.l1 constant
## ltxc.l1 1.0000000 1.00000000 1.00000000 1.00000000 1.000000
## lpgi.l1 0.9641571 1.02136550 0.98695687 1.17866752 1.430740
## lpsb.l1 -0.8624352 -0.97270279 -1.00371557 -0.99276683 -1.022931
## legq.l1 -0.0851317 0.04262155 0.04923599 -0.03428208 0.161438
## constant 1.0025091 -1.08181690 -0.91181119 -0.09484798 -3.986988
##
## Weights W:
## (This is the loading matrix)
##
## ltxc.l1 lpgi.l1 lpsb.l1 legq.l1 constant
## ltxc.d -3.1444446 -3.6271234 1.6404286 1.2011785 2.970897e-11
## lpgi.d 0.4023547 -0.4982545 1.3953772 -1.3133013 1.390835e-12
## lpsb.d -2.6926051 -4.1235637 4.3242985 0.1689927 2.041034e-11
## legq.d 0.3318604 -3.0523679 -0.6347919 1.3235401 8.802178e-12
#Traço longo prazo
jotest_traco_lp <- ca.jo((dados_ts), type="trace", K=3, ecdet = "const", spec="longrun",
season = NULL, dumvar = NULL) # Há até três níveis de cointegração
summary(jotest_traco_lp)
##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , without linear trend and constant in cointegration
##
## Eigenvalues (lambda):
## [1] 9.359966e-01 7.015766e-01 3.490419e-01 2.317578e-01 -9.264453e-16
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 3 | 8.17 7.52 9.24 12.97
## r <= 2 | 21.48 17.85 19.96 24.60
## r <= 1 | 58.97 32.00 34.91 41.07
## r = 0 | 144.18 49.65 53.12 60.16
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## ltxc.l3 lpgi.l3 lpsb.l3 legq.l3 constant
## ltxc.l3 1.0000000 1.00000000 1.00000000 1.00000000 1.000000
## lpgi.l3 0.9641571 1.02136550 0.98695687 1.17866752 1.430740
## lpsb.l3 -0.8624352 -0.97270279 -1.00371557 -0.99276683 -1.022931
## legq.l3 -0.0851317 0.04262155 0.04923599 -0.03428208 0.161438
## constant 1.0025091 -1.08181690 -0.91181119 -0.09484798 -3.986988
##
## Weights W:
## (This is the loading matrix)
##
## ltxc.l3 lpgi.l3 lpsb.l3 legq.l3 constant
## ltxc.d -3.1444446 -3.6271234 1.6404286 1.2011785 7.550175e-11
## lpgi.d 0.4023547 -0.4982545 1.3953772 -1.3133013 5.459337e-12
## lpsb.d -2.6926052 -4.1235637 4.3242985 0.1689927 5.089868e-11
## legq.d 0.3318604 -3.0523679 -0.6347919 1.3235401 2.880411e-11
#Raíz máxima transitório
jotest_max_tr <- ca.jo((dados_ts), type="eigen", K=3, ecdet = "const", spec="transitory",
season = NULL, dumvar = NULL) # Há até dois níveis de cointegração
summary(jotest_max_tr)
##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: maximal eigenvalue statistic (lambda max) , without linear trend and constant in cointegration
##
## Eigenvalues (lambda):
## [1] 9.359966e-01 7.015766e-01 3.490419e-01 2.317578e-01 2.070216e-16
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 3 | 8.17 7.52 9.24 12.97
## r <= 2 | 13.31 13.75 15.67 20.20
## r <= 1 | 37.49 19.77 22.00 26.81
## r = 0 | 85.21 25.56 28.14 33.24
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## ltxc.l1 lpgi.l1 lpsb.l1 legq.l1 constant
## ltxc.l1 1.0000000 1.00000000 1.00000000 1.00000000 1.000000
## lpgi.l1 0.9641571 1.02136550 0.98695687 1.17866752 1.430740
## lpsb.l1 -0.8624352 -0.97270279 -1.00371557 -0.99276683 -1.022931
## legq.l1 -0.0851317 0.04262155 0.04923599 -0.03428208 0.161438
## constant 1.0025091 -1.08181690 -0.91181119 -0.09484798 -3.986988
##
## Weights W:
## (This is the loading matrix)
##
## ltxc.l1 lpgi.l1 lpsb.l1 legq.l1 constant
## ltxc.d -3.1444446 -3.6271234 1.6404286 1.2011785 2.970897e-11
## lpgi.d 0.4023547 -0.4982545 1.3953772 -1.3133013 1.390835e-12
## lpsb.d -2.6926051 -4.1235637 4.3242985 0.1689927 2.041034e-11
## legq.d 0.3318604 -3.0523679 -0.6347919 1.3235401 8.802178e-12
#Raíz máxima longo prazo
jotest_max_lp <- ca.jo((dados_ts), type="eigen", K=3, ecdet = "const", spec="longrun",
season = NULL, dumvar = NULL) # Há até dois níveis de cointegração
summary(jotest_max_lp)
##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: maximal eigenvalue statistic (lambda max) , without linear trend and constant in cointegration
##
## Eigenvalues (lambda):
## [1] 9.359966e-01 7.015766e-01 3.490419e-01 2.317578e-01 -9.264453e-16
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 3 | 8.17 7.52 9.24 12.97
## r <= 2 | 13.31 13.75 15.67 20.20
## r <= 1 | 37.49 19.77 22.00 26.81
## r = 0 | 85.21 25.56 28.14 33.24
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## ltxc.l3 lpgi.l3 lpsb.l3 legq.l3 constant
## ltxc.l3 1.0000000 1.00000000 1.00000000 1.00000000 1.000000
## lpgi.l3 0.9641571 1.02136550 0.98695687 1.17866752 1.430740
## lpsb.l3 -0.8624352 -0.97270279 -1.00371557 -0.99276683 -1.022931
## legq.l3 -0.0851317 0.04262155 0.04923599 -0.03428208 0.161438
## constant 1.0025091 -1.08181690 -0.91181119 -0.09484798 -3.986988
##
## Weights W:
## (This is the loading matrix)
##
## ltxc.l3 lpgi.l3 lpsb.l3 legq.l3 constant
## ltxc.d -3.1444446 -3.6271234 1.6404286 1.2011785 7.550175e-11
## lpgi.d 0.4023547 -0.4982545 1.3953772 -1.3133013 5.459337e-12
## lpsb.d -2.6926052 -4.1235637 4.3242985 0.1689927 5.089868e-11
## legq.d 0.3318604 -3.0523679 -0.6347919 1.3235401 2.880411e-11
##Modelo VEC é mais adequado
#VEC
vec <- cajorls(jotest_traco_lp, r=3, reg.number = NULL)
vec
## $rlm
##
## Call:
## lm(formula = substitute(form1), data = data.mat)
##
## Coefficients:
## ltxc.d lpgi.d lpsb.d legq.d
## ect1 -5.1311 1.2995 -2.4919 -3.3553
## ect2 -5.1173 1.2562 -2.5399 -3.4241
## ect3 4.5935 -1.2629 1.9928 3.3200
## ltxc.dl1 -1.3230 -0.6540 -0.8056 -1.2707
## lpgi.dl1 -1.1616 -0.4717 -0.4578 -1.2561
## lpsb.dl1 0.8892 0.7724 0.4895 1.1834
## legq.dl1 0.1477 -0.3680 -0.1557 -0.5555
## ltxc.dl2 -3.1351 -0.7865 -2.6427 -2.2617
## lpgi.dl2 -2.9379 -1.1680 -2.8733 -2.2704
## lpsb.dl2 2.5760 0.7911 2.1022 2.0932
## legq.dl2 0.6551 -0.1728 0.4915 -0.4717
##
##
## $beta
## ect1 ect2 ect3
## ltxc.l3 1.000000e+00 0.0000000 0.000000e+00
## lpgi.l3 1.776357e-15 1.0000000 1.776357e-15
## lpsb.l3 1.776357e-15 0.0000000 1.000000e+00
## legq.l3 -1.384298e+00 0.5805358 -8.573848e-01
## constant 2.504250e+01 -14.9751523 1.113311e+01
summary(vec$rlm)
## Response ltxc.d :
##
## Call:
## lm(formula = ltxc.d ~ ect1 + ect2 + ect3 + ltxc.dl1 + lpgi.dl1 +
## lpsb.dl1 + legq.dl1 + ltxc.dl2 + lpgi.dl2 + lpsb.dl2 + legq.dl2 -
## 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.3406 -0.1231 -0.0420 0.1002 0.5124
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 -5.1311 2.1482 -2.389 0.0269 *
## ect2 -5.1173 2.1295 -2.403 0.0261 *
## ect3 4.5935 2.1365 2.150 0.0440 *
## ltxc.dl1 -1.3230 1.1221 -1.179 0.2522
## lpgi.dl1 -1.1616 1.1077 -1.049 0.3068
## lpsb.dl1 0.8892 1.1041 0.805 0.4301
## legq.dl1 0.1477 0.2874 0.514 0.6130
## ltxc.dl2 -3.1351 1.6297 -1.924 0.0687 .
## lpgi.dl2 -2.9379 1.6089 -1.826 0.0828 .
## lpsb.dl2 2.5760 1.6116 1.598 0.1256
## legq.dl2 0.6551 0.2491 2.630 0.0161 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.223 on 20 degrees of freedom
## Multiple R-squared: 0.9466, Adjusted R-squared: 0.9172
## F-statistic: 32.2 on 11 and 20 DF, p-value: 2.679e-10
##
##
## Response lpgi.d :
##
## Call:
## lm(formula = lpgi.d ~ ect1 + ect2 + ect3 + ltxc.dl1 + lpgi.dl1 +
## lpsb.dl1 + legq.dl1 + ltxc.dl2 + lpgi.dl2 + lpsb.dl2 + legq.dl2 -
## 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.21839 -0.08084 0.00095 0.06965 0.32607
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 1.2995 1.4141 0.919 0.369
## ect2 1.2562 1.4019 0.896 0.381
## ect3 -1.2629 1.4065 -0.898 0.380
## ltxc.dl1 -0.6540 0.7387 -0.885 0.386
## lpgi.dl1 -0.4717 0.7292 -0.647 0.525
## lpsb.dl1 0.7724 0.7268 1.063 0.301
## legq.dl1 -0.3680 0.1892 -1.945 0.066 .
## ltxc.dl2 -0.7865 1.0728 -0.733 0.472
## lpgi.dl2 -1.1680 1.0591 -1.103 0.283
## lpsb.dl2 0.7911 1.0609 0.746 0.465
## legq.dl2 -0.1728 0.1640 -1.053 0.305
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1468 on 20 degrees of freedom
## Multiple R-squared: 0.5393, Adjusted R-squared: 0.286
## F-statistic: 2.129 on 11 and 20 DF, p-value: 0.06845
##
##
## Response lpsb.d :
##
## Call:
## lm(formula = lpsb.d ~ ect1 + ect2 + ect3 + ltxc.dl1 + lpgi.dl1 +
## lpsb.dl1 + legq.dl1 + ltxc.dl2 + lpgi.dl2 + lpsb.dl2 + legq.dl2 -
## 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.36190 -0.12161 -0.01369 0.12101 0.52469
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 -2.4919 2.3072 -1.080 0.2930
## ect2 -2.5399 2.2872 -1.110 0.2800
## ect3 1.9928 2.2947 0.868 0.3954
## ltxc.dl1 -0.8056 1.2051 -0.668 0.5115
## lpgi.dl1 -0.4578 1.1897 -0.385 0.7045
## lpsb.dl1 0.4895 1.1858 0.413 0.6842
## legq.dl1 -0.1557 0.3087 -0.504 0.6195
## ltxc.dl2 -2.6427 1.7503 -1.510 0.1467
## lpgi.dl2 -2.8733 1.7280 -1.663 0.1120
## lpsb.dl2 2.1022 1.7309 1.214 0.2387
## legq.dl2 0.4915 0.2676 1.837 0.0812 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2395 on 20 degrees of freedom
## Multiple R-squared: 0.941, Adjusted R-squared: 0.9085
## F-statistic: 28.99 on 11 and 20 DF, p-value: 7.054e-10
##
##
## Response legq.d :
##
## Call:
## lm(formula = legq.d ~ ect1 + ect2 + ect3 + ltxc.dl1 + lpgi.dl1 +
## lpsb.dl1 + legq.dl1 + ltxc.dl2 + lpgi.dl2 + lpsb.dl2 + legq.dl2 -
## 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.22271 -0.12129 -0.03810 0.08488 0.35704
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 -3.3553 1.7762 -1.889 0.0735 .
## ect2 -3.4241 1.7607 -1.945 0.0660 .
## ect3 3.3200 1.7665 1.879 0.0748 .
## ltxc.dl1 -1.2707 0.9277 -1.370 0.1860
## lpgi.dl1 -1.2561 0.9159 -1.371 0.1854
## lpsb.dl1 1.1834 0.9129 1.296 0.2096
## legq.dl1 -0.5555 0.2377 -2.337 0.0299 *
## ltxc.dl2 -2.2617 1.3474 -1.679 0.1088
## lpgi.dl2 -2.2704 1.3303 -1.707 0.1034
## lpsb.dl2 2.0932 1.3325 1.571 0.1319
## legq.dl2 -0.4717 0.2060 -2.290 0.0330 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1843 on 20 degrees of freedom
## Multiple R-squared: 0.5702, Adjusted R-squared: 0.3338
## F-statistic: 2.412 on 11 and 20 DF, p-value: 0.04199
##Função impulso resposta
varvec <- vars::vec2var(jotest_traco_lp, r=3)
##Estabilidade: todas as a raizes dentro do circulo unitário
eigen <- eigen(varvec$A$A1)
eigen
## eigen() decomposition
## $values
## [1] 1.2710382+0.0000000i 0.5797077+0.0790627i 0.5797077-0.0790627i
## [4] -0.2911435+0.0000000i
##
## $vectors
## [,1] [,2] [,3] [,4]
## [1,] 0.32015137+0i 0.6911545+0.0000000i 0.6911545+0.0000000i 0.4178379+0i
## [2,] -0.80985948+0i -0.2385976+0.1391077i -0.2385976-0.1391077i 0.3503888+0i
## [3,] -0.49018584+0i 0.4326654+0.1764031i 0.4326654-0.1764031i 0.3458903+0i
## [4,] 0.03672281+0i -0.2570265+0.4020519i -0.2570265-0.4020519i 0.7635438+0i
#Impacto da taxa de câmbio no volume de exportações
impulso_ltxc_legq = irf(varvec, impulse = "ltxc", response = c('legq'), n.ahead = 5,
ortho = FALSE, cumulative = FALSE, boot = TRUE, ci = 0.95,
runs = 100, seed = NULL)
plot(impulso_ltxc_legq)
#Impacto do preço internacional da soja em grão no volume de exportações
impulso_lpgi_legq = irf(varvec, impulse = "lpgi", response = c('legq'), n.ahead = 5,
ortho = FALSE, cumulative = FALSE, boot = TRUE, ci = 0.95,
runs = 100, seed = NULL)
plot(impulso_lpgi_legq)
#Impacto do preço doméstico da soja em grão no volume de exportações
impulso_lpsb_legq=irf(varvec, impulse = "lpsb", response = c('legq'), n.ahead = 5,
ortho = FALSE, cumulative = FALSE, boot = TRUE, ci = 0.95,
runs = 100, seed = NULL)
plot(impulso_lpsb_legq)
##Decomposição do erro da variância
fevd(varvec, n.ahead = 5)$legq*100
## ltxc lpgi lpsb legq
## [1,] 60.53591 13.44869 1.329510 24.68589
## [2,] 58.92819 13.72240 5.480429 21.86898
## [3,] 54.78915 16.84394 7.961335 20.40557
## [4,] 56.08863 17.25873 9.193670 17.45897
## [5,] 56.67688 18.11762 8.296811 16.90869
fevd(varvec, n.ahead = 5)$ltxc*100
## ltxc lpgi lpsb legq
## [1,] 100.00000 0.000000 0.000000 0.0000000
## [2,] 95.54069 2.615012 1.637906 0.2063868
## [3,] 80.30197 12.394109 4.051867 3.2520571
## [4,] 67.96598 18.700156 10.455921 2.8779439
## [5,] 60.83345 26.253177 10.072762 2.8406158
fevd(varvec, n.ahead = 5)$lpgi*100
## ltxc lpgi lpsb legq
## [1,] 15.09406 84.90594 0.000000 0.000000
## [2,] 13.53913 82.16223 2.693134 1.605502
## [3,] 13.44498 81.33231 2.959053 2.263660
## [4,] 14.90590 75.19636 8.064458 1.833281
## [5,] 17.89786 68.47191 12.109412 1.520818
fevd(varvec, n.ahead = 5)$lpsb*100
## ltxc lpgi lpsb legq
## [1,] 65.04611 31.20022 3.753671 0.0000000
## [2,] 51.26181 40.91575 7.613079 0.2093539
## [3,] 56.39765 28.49798 14.027955 1.0764222
## [4,] 57.82171 26.47349 13.629626 2.0751734
## [5,] 55.67555 28.72184 12.906914 2.6956962
##Ajustamento
#Heterocedasticia
ARCH<-arch.test(varvec,lags.single = 4,lags.multi=2,multivariate.only=FALSE)
ARCH
## $`resids of ltxc`
##
## ARCH test (univariate)
##
## data: Residual of resids of ltxc equation
## Chi-squared = 14.988, df = 4, p-value = 0.004727
##
##
## $`resids of lpgi`
##
## ARCH test (univariate)
##
## data: Residual of resids of lpgi equation
## Chi-squared = 8.4084, df = 4, p-value = 0.07771
##
##
## $`resids of lpsb`
##
## ARCH test (univariate)
##
## data: Residual of resids of lpsb equation
## Chi-squared = 1.1823, df = 4, p-value = 0.881
##
##
## $`resids of legq`
##
## ARCH test (univariate)
##
## data: Residual of resids of legq equation
## Chi-squared = 7.066, df = 4, p-value = 0.1324
##
##
##
## ARCH (multivariate)
##
## data: Residuals of VAR object varvec
## Chi-squared = 189.13, df = 200, p-value = 0.6986
#Autocorrelação
vars::serial.test(varvec, type=c('PT.asymptotic'))
##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object varvec
## Chi-squared = 171.81, df = 212, p-value = 0.9802
#Normalidade
vars::normality.test(varvec, multivariate.only=TRUE)
## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object varvec
## Chi-squared = 13.011, df = 8, p-value = 0.1115
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object varvec
## Chi-squared = 10.717, df = 4, p-value = 0.02993
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object varvec
## Chi-squared = 2.2943, df = 4, p-value = 0.6818
##Exogeneidade
#Fraca --> Maioria dos alfas estatisticamente não-nulos
#Forte --> Um alfa estatisticamente nulo --> Teste de Granger-Causalidade:
grangertest(ltxc,legq,order=1)
## Granger causality test
##
## Model 1: legq ~ Lags(legq, 1:1) + Lags(ltxc, 1:1)
## Model 2: legq ~ Lags(legq, 1:1)
## Res.Df Df F Pr(>F)
## 1 30
## 2 31 -1 3.066 0.09016 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
grangertest(lpgi,legq,order=1)
## Granger causality test
##
## Model 1: legq ~ Lags(legq, 1:1) + Lags(lpgi, 1:1)
## Model 2: legq ~ Lags(legq, 1:1)
## Res.Df Df F Pr(>F)
## 1 30
## 2 31 -1 0.7683 0.3877
grangertest(lpsb,legq,order=1)
## Granger causality test
##
## Model 1: legq ~ Lags(legq, 1:1) + Lags(lpsb, 1:1)
## Model 2: legq ~ Lags(legq, 1:1)
## Res.Df Df F Pr(>F)
## 1 30
## 2 31 -1 3.7747 0.06147 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
var <- VAR(dados_ts, p = 1, type = "const", season = NULL, exogen = NULL)
causality(var, cause = "ltxc", vcov. = vcovHC(var))
## $Granger
##
## Granger causality H0: ltxc do not Granger-cause lpgi lpsb legq
##
## data: VAR object var
## F-Test = 0.71164, df1 = 3, df2 = 112, p-value = 0.547
##
##
## $Instant
##
## H0: No instantaneous causality between: ltxc and lpgi lpsb legq
##
## data: VAR object var
## Chi-squared = 16.419, df = 3, p-value = 0.0009302
causality(var, cause = "lpgi", vcov. = vcovHC(var))
## $Granger
##
## Granger causality H0: lpgi do not Granger-cause ltxc lpsb legq
##
## data: VAR object var
## F-Test = 0.45772, df1 = 3, df2 = 112, p-value = 0.7124
##
##
## $Instant
##
## H0: No instantaneous causality between: lpgi and ltxc lpsb legq
##
## data: VAR object var
## Chi-squared = 15.928, df = 3, p-value = 0.001173
causality(var, cause = "lpsb", vcov. = vcovHC(var))
## $Granger
##
## Granger causality H0: lpsb do not Granger-cause ltxc lpgi legq
##
## data: VAR object var
## F-Test = 0.74059, df1 = 3, df2 = 112, p-value = 0.53
##
##
## $Instant
##
## H0: No instantaneous causality between: lpsb and ltxc lpgi legq
##
## data: VAR object var
## Chi-squared = 16.425, df = 3, p-value = 0.0009276
##PREVISÃO
predict(varvec, n.ahead = 5, ci = 0.95, dumvar = NULL)
## $ltxc
## fcst lower upper CI
## [1,] 1.406332 1.0553447 1.757320 0.3509877
## [2,] 1.411509 0.9427035 1.880314 0.4688054
## [3,] 1.223078 0.5612847 1.884871 0.6617932
## [4,] 1.437568 0.6276292 2.247507 0.8099388
## [5,] 1.510488 0.6077739 2.413202 0.9027138
##
## $lpgi
## fcst lower upper CI
## [1,] 3.190535 2.959480 3.421590 0.2310548
## [2,] 3.068945 2.650155 3.487735 0.4187902
## [3,] 3.422752 2.916033 3.929472 0.5067196
## [4,] 3.531599 2.965157 4.098040 0.5664414
## [5,] 3.454026 2.822880 4.085173 0.6311464
##
## $lpsb
## fcst lower upper CI
## [1,] 4.552338 4.175367 4.929309 0.3769713
## [2,] 4.402563 3.911890 4.893235 0.4906721
## [3,] 4.599371 4.008663 5.190079 0.5907080
## [4,] 4.905638 4.265407 5.545869 0.6402313
## [5,] 4.898010 4.235884 5.560135 0.6621254
##
## $legq
## fcst lower upper CI
## [1,] 18.34261 18.05241 18.63282 0.2902052
## [2,] 18.40954 18.07211 18.74696 0.3374223
## [3,] 18.42615 18.05724 18.79506 0.3689129
## [4,] 18.57016 18.13832 19.00200 0.4318390
## [5,] 18.56540 18.10274 19.02805 0.4626558