# install.packages(c("vars", "urca", "tseries", "ggplot2", "gridExtra"))
library(vars)
## Cargando paquete requerido: MASS
## Cargando paquete requerido: strucchange
## Cargando paquete requerido: zoo
##
## Adjuntando el paquete: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Cargando paquete requerido: sandwich
## Cargando paquete requerido: urca
## Cargando paquete requerido: lmtest
library(urca)
library(tseries)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(ggplot2)
library(gridExtra)
############################################################
# 1. SIMULACIÓN DE DATOS
############################################################
set.seed(123)
n <- 200
# Generamos 3 series con cierta relación entre ellas
e1 <- rnorm(n)
e2 <- rnorm(n)
e3 <- rnorm(n)
y1 <- cumsum(e1)
y2 <- 0.5 * y1 + cumsum(e2)
y3 <- 0.3 * y1 + 0.2 * y2 + cumsum(e3)
data <- data.frame(y1, y2, y3)
############################################################
# 2. GRÁFICAS DE LAS SERIES
############################################################
g1 <- ggplot(data, aes(x = 1:n, y = y1)) +
geom_line(color = "blue") +
ggtitle("Serie y1")
g2 <- ggplot(data, aes(x = 1:n, y = y2)) +
geom_line(color = "red") +
ggtitle("Serie y2")
g3 <- ggplot(data, aes(x = 1:n, y = y3)) +
geom_line(color = "green") +
ggtitle("Serie y3")
grid.arrange(g1, g2, g3, ncol = 1)
############################################################
# 3. PRUEBAS DE ESTACIONARIEDAD (ADF)
############################################################
adf.test(y1)
##
## Augmented Dickey-Fuller Test
##
## data: y1
## Dickey-Fuller = -2.2954, Lag order = 5, p-value = 0.4524
## alternative hypothesis: stationary
adf.test(y2)
##
## Augmented Dickey-Fuller Test
##
## data: y2
## Dickey-Fuller = -1.8185, Lag order = 5, p-value = 0.6521
## alternative hypothesis: stationary
adf.test(y3)
##
## Augmented Dickey-Fuller Test
##
## data: y3
## Dickey-Fuller = -0.69396, Lag order = 5, p-value = 0.9696
## alternative hypothesis: stationary
# Normalmente serán no estacionarias → diferenciar
dy1 <- diff(y1)
dy2 <- diff(y2)
dy3 <- diff(y3)
############################################################
# 4. SELECCIÓN DE REZAGOS PARA VAR
############################################################
data_diff <- na.omit(data.frame(dy1, dy2, dy3))
lagselect <- VARselect(data_diff, lag.max = 10, type = "const")
lagselect$criteria
## 1 2 3 4 5 6
## AIC(n) -0.089412744 -0.02552013 0.02077339 0.03621041 0.07000952 0.07541474
## HQ(n) -0.006028002 0.12040317 0.22923525 0.30721083 0.40354849 0.47149227
## SC(n) 0.116412464 0.33467398 0.53533641 0.70514234 0.89331035 1.05308448
## FPE(n) 0.914485397 0.97490189 1.02129367 1.03755098 1.07382621 1.08053800
## 7 8 9 10
## AIC(n) 0.1357496 0.2009560 0.2363948 0.2991204
## HQ(n) 0.5943657 0.7221106 0.8200880 0.9453521
## SC(n) 1.2677882 1.4873635 1.6771712 1.8942657
## FPE(n) 1.1490435 1.2283035 1.2750493 1.3608247
############################################################
# 5. MODELO VAR
############################################################
var_model <- VAR(data_diff, p = 2, type = "const")
summary(var_model)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: dy1, dy2, dy3
## Deterministic variables: const
## Sample size: 197
## Log Likelihood: -811.329
## Roots of the characteristic polynomial:
## 0.3071 0.3071 0.3019 0.3019 0.127 0.04695
## Call:
## VAR(y = data_diff, p = 2, type = "const")
##
##
## Estimation results for equation dy1:
## ====================================
## dy1 = dy1.l1 + dy2.l1 + dy3.l1 + dy1.l2 + dy2.l2 + dy3.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## dy1.l1 -0.07781 0.08172 -0.952 0.342
## dy2.l1 0.04985 0.06962 0.716 0.475
## dy3.l1 -0.02636 0.07096 -0.372 0.711
## dy1.l2 -0.07612 0.08169 -0.932 0.353
## dy2.l2 -0.06299 0.06969 -0.904 0.367
## dy3.l2 0.05774 0.07108 0.812 0.418
## const -0.01161 0.06765 -0.172 0.864
##
##
## Residual standard error: 0.9476 on 190 degrees of freedom
## Multiple R-Squared: 0.0207, Adjusted R-squared: -0.01023
## F-statistic: 0.6692 on 6 and 190 DF, p-value: 0.6746
##
##
## Estimation results for equation dy2:
## ====================================
## dy2 = dy1.l1 + dy2.l1 + dy3.l1 + dy1.l2 + dy2.l2 + dy3.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## dy1.l1 0.011035 0.094613 0.117 0.907
## dy2.l1 0.008654 0.080612 0.107 0.915
## dy3.l1 -0.069874 0.082156 -0.851 0.396
## dy1.l2 0.042985 0.094583 0.454 0.650
## dy2.l2 -0.067277 0.080682 -0.834 0.405
## dy3.l2 0.059986 0.082298 0.729 0.467
## const 0.023239 0.078323 0.297 0.767
##
##
## Residual standard error: 1.097 on 190 degrees of freedom
## Multiple R-Squared: 0.01119, Adjusted R-squared: -0.02003
## F-statistic: 0.3585 on 6 and 190 DF, p-value: 0.9043
##
##
## Estimation results for equation dy3:
## ====================================
## dy3 = dy1.l1 + dy2.l1 + dy3.l1 + dy1.l2 + dy2.l2 + dy3.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## dy1.l1 -0.01165 0.09030 -0.129 0.897
## dy2.l1 0.03440 0.07693 0.447 0.655
## dy3.l1 -0.11418 0.07841 -1.456 0.147
## dy1.l2 0.02235 0.09027 0.248 0.805
## dy2.l2 0.02897 0.07700 0.376 0.707
## dy3.l2 -0.01984 0.07854 -0.253 0.801
## const 0.04433 0.07475 0.593 0.554
##
##
## Residual standard error: 1.047 on 190 degrees of freedom
## Multiple R-Squared: 0.01378, Adjusted R-squared: -0.01736
## F-statistic: 0.4425 on 6 and 190 DF, p-value: 0.8497
##
##
##
## Covariance matrix of residuals:
## dy1 dy2 dy3
## dy1 0.8979 0.4345 0.3367
## dy2 0.4345 1.2037 0.3129
## dy3 0.3367 0.3129 1.0964
##
## Correlation matrix of residuals:
## dy1 dy2 dy3
## dy1 1.0000 0.4179 0.3394
## dy2 0.4179 1.0000 0.2724
## dy3 0.3394 0.2724 1.0000
############################################################
# 6. CAUSALIDAD DE GRANGER
############################################################
# ¿y2 causa a y1?
granger_y2_y1 <- causality(var_model, cause = "dy2")
print(granger_y2_y1)
## $Granger
##
## Granger causality H0: dy2 do not Granger-cause dy1 dy3
##
## data: VAR object var_model
## F-Test = 0.48204, df1 = 4, df2 = 570, p-value = 0.7489
##
##
## $Instant
##
## H0: No instantaneous causality between: dy2 and dy1 dy3
##
## data: VAR object var_model
## Chi-squared = 31.997, df = 2, p-value = 1.127e-07
# ¿y1 causa a y2?
granger_y1_y2 <- causality(var_model, cause = "dy1")
print(granger_y1_y2)
## $Granger
##
## Granger causality H0: dy1 do not Granger-cause dy2 dy3
##
## data: VAR object var_model
## F-Test = 0.065325, df1 = 4, df2 = 570, p-value = 0.9922
##
##
## $Instant
##
## H0: No instantaneous causality between: dy1 and dy2 dy3
##
## data: VAR object var_model
## Chi-squared = 36.783, df = 2, p-value = 1.03e-08
############################################################
# 7. GRÁFICAS: FUNCIONES IMPULSO-RESPUESTA
############################################################
irf_result <- irf(var_model, impulse = "dy1", response = "dy2", n.ahead = 10, boot = TRUE)
plot(irf_result)
############################################################
# 8. PRUEBA DE COINTEGRACIÓN DE JOHANSEN
############################################################
# Usamos los datos en niveles
johansen_test <- ca.jo(data, type = "trace", ecdet = "const", K = 2)
summary(johansen_test)
##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , without linear trend and constant in cointegration
##
## Eigenvalues (lambda):
## [1] 8.137096e-02 3.762205e-02 9.645518e-03 4.327346e-19
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 2 | 1.92 7.52 9.24 12.97
## r <= 1 | 9.51 17.85 19.96 24.60
## r = 0 | 26.32 32.00 34.91 41.07
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## y1.l2 y2.l2 y3.l2 constant
## y1.l2 1.00000 1.0000000 1.0000000 1.0000000
## y2.l2 27.41840 -0.1224349 -0.2961117 -0.5281511
## y3.l2 -20.63583 0.2753543 -0.6755809 -0.6990262
## constant -70.12262 -2.9265132 9.3488089 -3.8004592
##
## Weights W:
## (This is the loading matrix)
##
## y1.l2 y2.l2 y3.l2 constant
## y1.d -0.0024501104 -0.045267154 -0.004166726 -1.045478e-17
## y2.d -0.0044105866 0.006384182 0.004580397 -2.038217e-17
## y3.d -0.0005113845 -0.044872784 0.010822444 -4.288473e-19
############################################################
# 9. MODELO VECM
############################################################
vecm_model <- cajorls(johansen_test, r = 1) # r = número de relaciones de cointegración
summary(vecm_model$rlm)
## Response y1.d :
##
## Call:
## lm(formula = y1.d ~ ect1 + y1.dl1 + y2.dl1 + y3.dl1 - 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.47332 -0.66489 -0.03653 0.59182 2.92279
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 -0.002450 0.001003 -2.443 0.0154 *
## y1.dl1 -0.090513 0.080547 -1.124 0.2625
## y2.dl1 0.022443 0.069903 0.321 0.7485
## y3.dl1 -0.027826 0.069669 -0.399 0.6900
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9357 on 194 degrees of freedom
## Multiple R-squared: 0.03856, Adjusted R-squared: 0.01874
## F-statistic: 1.945 on 4 and 194 DF, p-value: 0.1045
##
##
## Response y2.d :
##
## Call:
## lm(formula = y2.d ~ ect1 + y1.dl1 + y2.dl1 + y3.dl1 - 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.54472 -0.63137 -0.09289 0.72364 2.82058
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 -0.004411 0.001124 -3.923 0.000121 ***
## y1.dl1 -0.018630 0.090306 -0.206 0.836777
## y2.dl1 -0.054010 0.078372 -0.689 0.491556
## y3.dl1 -0.054515 0.078110 -0.698 0.486056
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.049 on 194 degrees of freedom
## Multiple R-squared: 0.07824, Adjusted R-squared: 0.05924
## F-statistic: 4.117 on 4 and 194 DF, p-value: 0.003175
##
##
## Response y3.d :
##
## Call:
## lm(formula = y3.d ~ ect1 + y1.dl1 + y2.dl1 + y3.dl1 - 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0091 -0.6482 0.0961 0.6689 3.1905
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 -0.0005114 0.0011120 -0.460 0.646
## y1.dl1 -0.0156219 0.0893191 -0.175 0.861
## y2.dl1 0.0262895 0.0775161 0.339 0.735
## y3.dl1 -0.1065429 0.0772565 -1.379 0.169
##
## Residual standard error: 1.038 on 194 degrees of freedom
## Multiple R-squared: 0.01279, Adjusted R-squared: -0.007567
## F-statistic: 0.6282 on 4 and 194 DF, p-value: 0.6429
############################################################
# 10. INTERPRETACIÓN
############################################################
# - Prueba de Granger:
# Evalúa si una variable ayuda a predecir otra.
# Si p-value < 0.05 → hay causalidad en sentido de Granger.
# - VAR:
# Modelo de variables endógenas donde todas dependen de sus rezagos y de las otras.
# - Johansen:
# Detecta cointegración (relaciones de largo plazo).
# Usa dos tests:
# * Trace
# * Eigenvalue
# - VECM:
# Se usa cuando hay cointegración.
# Incluye:
# * dinámica de corto plazo
# * corrección de error (equilibrio de largo plazo)