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library(tidyverse)
library(forecast)
library(quantmod)
library(AER)
library(MASS)
library(tseries)
library(stats)
library(car)
library(lmtest)
library(urca)
# 1. Caminatas Aleatorias
set.seed(180188)
n <- 240
u <- rnorm(n)
v <- rnorm(n)
X <- numeric(n)
Y <- numeric(n)
for (t in 2:n) {
X[t] <- X[t-1] + u[t]
Y[t] <- Y[t-1] + v[t]
}
data <- data.frame(X, Y)
# 2. Regresión Lineal
modelo <- lm(Y ~ X, data=data)
summary(modelo)
##
## Call:
## lm(formula = Y ~ X, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.0492 -3.3070 -0.0299 2.5518 14.4081
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.03357 0.28586 17.61 <2e-16 ***
## X 1.29574 0.08664 14.96 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.365 on 238 degrees of freedom
## Multiple R-squared: 0.4845, Adjusted R-squared: 0.4823
## F-statistic: 223.7 on 1 and 238 DF, p-value: < 2.2e-16
# 3. Pruebas de Estacionariedad (ADF)
adf.test(X)
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## Augmented Dickey-Fuller Test
##
## data: X
## Dickey-Fuller = -3.2472, Lag order = 6, p-value = 0.08071
## alternative hypothesis: stationary
adf.test(Y)
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## Augmented Dickey-Fuller Test
##
## data: Y
## Dickey-Fuller = -2.5759, Lag order = 6, p-value = 0.3337
## alternative hypothesis: stationary
# 4. Residuales y Cointegración
residuales <- residuals(modelo)
adf.test(residuales)
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## Augmented Dickey-Fuller Test
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## data: residuales
## Dickey-Fuller = -2.4605, Lag order = 6, p-value = 0.3822
## alternative hypothesis: stationary
# 5. ACF
acf(X)
acf(Y)
acf(residuales)
# 6. Análisis de Datos Macroeconómicos
data("USMacroSWM", package = "AER")
# Filtrado de datos 1948-2004
TS <- ts(USMacroSWM[-(1:12), 1:2], start=1948, freq=12)
colnames(TS) <- c("production", "oil")
# 7. Regresión Producción ~ Petróleo
modelo2 <- lm(production ~ oil, data=as.data.frame(TS))
summary(modelo2)
##
## Call:
## lm(formula = production ~ oil, data = as.data.frame(TS))
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.018 -26.163 -2.519 19.464 60.811
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 57.099 1.127 50.68 < 2e-16 ***
## oil 196.485 38.007 5.17 3.08e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 28.32 on 682 degrees of freedom
## Multiple R-squared: 0.03771, Adjusted R-squared: 0.0363
## F-statistic: 26.73 on 1 and 682 DF, p-value: 3.085e-07
# 8. Pruebas de Estacionariedad
adf.test(TS[, "production"])
##
## Augmented Dickey-Fuller Test
##
## data: TS[, "production"]
## Dickey-Fuller = -1.9631, Lag order = 8, p-value = 0.5939
## alternative hypothesis: stationary
adf.test(TS[, "oil"])
## Warning in adf.test(TS[, "oil"]): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: TS[, "oil"]
## Dickey-Fuller = -6.7672, Lag order = 8, p-value = 0.01
## alternative hypothesis: stationary
# 9. Residuales y Cointegración
residuales2 <- residuals(modelo2)
adf.test(residuales2)
##
## Augmented Dickey-Fuller Test
##
## data: residuales2
## Dickey-Fuller = -3.5316, Lag order = 8, p-value = 0.03927
## alternative hypothesis: stationary
acf(TS[, "production"])
acf(TS[, "oil"])
acf(residuales2)
