Laboratorio No. 8
Ricardo Cruz
2023-04-16
Cargamos las librerías
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coint <- read_excel("C:/Users/Ricardo Cruz/Desktop/Econometría II/01 Laboratorios/Cointegración en R.xls")
attach(coint)
names(coint)## [1] "Year" "Quarter" "tiempo" "DPI" "GDP" "PCE" "CP"
## [8] "DIVIDEND"class(coint)## [1] "tbl_df" "tbl" "data.frame"plot(PCE, type="l")
Crear variables de series de tiempo
Para este caso usaremos la variable GDP y a variable PCE empezando desde 1974 hasta 2007, en frecuency colocamos 4 porque son datos trimestrales.
GDP.ts = ts(GDP, start=c(1974,1), end=c(2007,4), frequency = 4)
PCE.ts = ts(PCE, start=c(1974,1), end=c(2007,4), frequency = 4)
datos1=cbind(GDP.ts, PCE.ts)
plot(cbind(GDP.ts, PCE.ts))
Cointegracion
Generar modelo
Revisamos por medio de la función cor la correlación que tienen las variables PCE y GDP. Después creamos un regresión con las mismas variables y extraemos por medio de selection el valor en P a utilizar que en este caso es 2.
cor(PCE, GDP)## [1] 0.9991024modelo1 = lm(PCE.ts ~ GDP.ts )
a <- VARselect(datos1,lag.max = 10,type="const");a$selection## AIC(n) HQ(n) SC(n) FPE(n)
## 2 2 2 2modelos = VAR(datos1, p=2)
summary(modelos)##
## VAR Estimation Results:
## =========================
## Endogenous variables: GDP.ts, PCE.ts
## Deterministic variables: const
## Sample size: 134
## Log Likelihood: -1208.96
## Roots of the characteristic polynomial:
## 1.006 0.9007 0.2847 0.1399
## Call:
## VAR(y = datos1, p = 2)
##
##
## Estimation results for equation GDP.ts:
## =======================================
## GDP.ts = GDP.ts.l1 + PCE.ts.l1 + GDP.ts.l2 + PCE.ts.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## GDP.ts.l1 0.96042 0.11155 8.610 2.19e-14 ***
## PCE.ts.l1 0.74110 0.20287 3.653 0.000375 ***
## GDP.ts.l2 -0.07072 0.11018 -0.642 0.522110
## PCE.ts.l2 -0.57426 0.20649 -2.781 0.006231 **
## const 24.30575 11.28947 2.153 0.033183 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 34.35 on 129 degrees of freedom
## Multiple R-Squared: 0.9991, Adjusted R-squared: 0.999
## F-statistic: 3.438e+04 on 4 and 129 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation PCE.ts:
## =======================================
## PCE.ts = GDP.ts.l1 + PCE.ts.l1 + GDP.ts.l2 + PCE.ts.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## GDP.ts.l1 0.05774 0.06454 0.895 0.373
## PCE.ts.l1 1.09123 0.11737 9.297 4.71e-16 ***
## GDP.ts.l2 -0.07105 0.06375 -1.115 0.267
## PCE.ts.l2 -0.06658 0.11947 -0.557 0.578
## const 6.63225 6.53169 1.015 0.312
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 19.87 on 129 degrees of freedom
## Multiple R-Squared: 0.9993, Adjusted R-squared: 0.9993
## F-statistic: 4.687e+04 on 4 and 129 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## GDP.ts PCE.ts
## GDP.ts 1179.6 460.4
## PCE.ts 460.4 394.9
##
## Correlation matrix of residuals:
## GDP.ts PCE.ts
## GDP.ts 1.0000 0.6745
## PCE.ts 0.6745 1.0000residuos <- resid(modelos)Prueba
adf.test(residuos[,1]) #usar esta## Augmented Dickey-Fuller Test
## alternative: stationary
##
## Type 1: no drift no trend
## lag ADF p.value
## [1,] 0 -12.28 0.01
## [2,] 1 -7.60 0.01
## [3,] 2 -6.48 0.01
## [4,] 3 -5.45 0.01
## [5,] 4 -4.67 0.01
## Type 2: with drift no trend
## lag ADF p.value
## [1,] 0 -12.23 0.01
## [2,] 1 -7.57 0.01
## [3,] 2 -6.45 0.01
## [4,] 3 -5.43 0.01
## [5,] 4 -4.65 0.01
## Type 3: with drift and trend
## lag ADF p.value
## [1,] 0 -12.19 0.01
## [2,] 1 -7.54 0.01
## [3,] 2 -6.43 0.01
## [4,] 3 -5.41 0.01
## [5,] 4 -4.63 0.01
## ----
## Note: in fact, p.value = 0.01 means p.value <= 0.01y = ur.df(residuos[,1], type = "trend", selectlags = "AIC")
summary(y)##
## ###############################################
## # 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
## -119.062 -19.577 0.652 19.013 147.063
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.54056 6.04531 -0.089 0.929
## z.lag.1 -0.98607 0.13083 -7.537 7.72e-12 ***
## tt 0.01280 0.07799 0.164 0.870
## z.diff.lag -0.08040 0.08887 -0.905 0.367
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 34.14 on 128 degrees of freedom
## Multiple R-squared: 0.535, Adjusted R-squared: 0.5241
## F-statistic: 49.1 on 3 and 128 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -7.5372 18.968 28.4248
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47adf.test(residuos[,2]) #usar esta## Augmented Dickey-Fuller Test
## alternative: stationary
##
## Type 1: no drift no trend
## lag ADF p.value
## [1,] 0 -11.61 0.01
## [2,] 1 -6.85 0.01
## [3,] 2 -5.54 0.01
## [4,] 3 -5.08 0.01
## [5,] 4 -5.03 0.01
## Type 2: with drift no trend
## lag ADF p.value
## [1,] 0 -11.57 0.01
## [2,] 1 -6.82 0.01
## [3,] 2 -5.52 0.01
## [4,] 3 -5.06 0.01
## [5,] 4 -5.02 0.01
## Type 3: with drift and trend
## lag ADF p.value
## [1,] 0 -11.54 0.01
## [2,] 1 -6.80 0.01
## [3,] 2 -5.50 0.01
## [4,] 3 -5.05 0.01
## [5,] 4 -5.00 0.01
## ----
## Note: in fact, p.value = 0.01 means p.value <= 0.01y = ur.df(residuos[,2], type = "trend", selectlags = "AIC")
summary(y)##
## ###############################################
## # 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
## -96.619 -7.803 0.418 10.804 41.779
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.69262 3.48200 -0.199 0.8426
## z.lag.1 -0.85702 0.12603 -6.800 3.58e-10 ***
## tt 0.01336 0.04492 0.298 0.7666
## z.diff.lag -0.15585 0.08825 -1.766 0.0798 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19.66 on 128 degrees of freedom
## Multiple R-squared: 0.5187, Adjusted R-squared: 0.5074
## F-statistic: 45.98 on 3 and 128 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -6.8002 15.443 23.1354
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -3.99 -3.43 -3.13
## phi2 6.22 4.75 4.07
## phi3 8.43 6.49 5.47Si el valor de p es menor a 0.05 es estacionaria las dos son estacionarias, por lo tanto hay cointegración, por lo tanto si hay relación a largo plazo.
El value of test-statistic tiene que ser menor a cualquier critial values for test statistics.
Philips y Oularis
El value of test-statistic tiene que ser menor a cualquier critial values for test statistics.
prueba.P0 = ca.po(datos1, type="Pz")
summary(prueba.P0)##
## ########################################
## # Phillips and Ouliaris Unit Root Test #
## ########################################
##
## Test of type Pz
## detrending of series none
##
## Response GDP.ts :
##
## Call:
## lm(formula = GDP.ts ~ zr - 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -150.279 -18.515 2.796 27.331 141.137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## zrGDP.ts 0.95334 0.03958 24.089 <2e-16 ***
## zrPCE.ts 0.08483 0.06116 1.387 0.168
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 37.23 on 133 degrees of freedom
## Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999
## F-statistic: 5.421e+05 on 2 and 133 DF, p-value: < 2.2e-16
##
##
## Response PCE.ts :
##
## Call:
## lm(formula = PCE.ts ~ zr - 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -104.417 -8.223 1.965 11.714 48.952
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## zrGDP.ts 0.007454 0.021281 0.35 0.727
## zrPCE.ts 0.996942 0.032886 30.32 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.02 on 133 degrees of freedom
## Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999
## F-statistic: 7.855e+05 on 2 and 133 DF, p-value: < 2.2e-16
##
##
##
## Value of test-statistic is: 13.4923
##
## Critical values of Pz are:
## 10pct 5pct 1pct
## critical values 33.9267 40.8217 55.1911prueba.P2 = ca.po(datos1, type="Pu")
summary(prueba.P2)##
## ########################################
## # Phillips and Ouliaris Unit Root Test #
## ########################################
##
## Test of type Pu
## detrending of series none
##
##
## Call:
## lm(formula = z[, 1] ~ z[, -1] - 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -185.94 -32.81 29.65 77.98 145.10
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z[, -1] 1.54450 0.00323 478.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 81.14 on 135 degrees of freedom
## Multiple R-squared: 0.9994, Adjusted R-squared: 0.9994
## F-statistic: 2.286e+05 on 1 and 135 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: 13.4278
##
## Critical values of Pu are:
## 10pct 5pct 1pct
## critical values 20.3933 25.9711 38.3413Según las pruebas se identificò que los residuos son estacionarios, entonces hay cointegración
Corrección de errores
Generación de tendencia si no están cointegrados
Cuando si hay cointegracion, hacemos las diferenciaciones
dlnPCE = diff(PCE.ts)
dlnGDP = diff(GDP.ts)
modelo3 = lm(dlnPCE~dlnGDP)
summary(modelo3)##
## Call:
## lm(formula = dlnPCE ~ dlnGDP)
##
## Residuals:
## Min 1Q Median 3Q Max
## -55.171 -6.835 -0.706 7.283 40.057
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.82308 1.58733 4.928 2.42e-06 ***
## dlnGDP 0.36719 0.03443 10.665 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.98 on 133 degrees of freedom
## Multiple R-squared: 0.461, Adjusted R-squared: 0.4569
## F-statistic: 113.7 on 1 and 133 DF, p-value: < 2.2e-16res3=modelo3$residuals
res3_1 = lag(res3)
MCE = lm(dlnPCE ~ dlnGDP + res3_1)
summary(MCE)##
## Call:
## lm(formula = dlnPCE ~ dlnGDP + res3_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.325 -6.831 -0.756 7.618 39.266
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.24990 1.61223 4.497 1.5e-05 ***
## dlnGDP 0.38558 0.03576 10.781 < 2e-16 ***
## res3_1 -0.15209 0.08988 -1.692 0.093 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.91 on 131 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.4742, Adjusted R-squared: 0.4661
## F-statistic: 59.06 on 2 and 131 DF, p-value: < 2.2e-16MCE$coefficients[3]## res3_1
## -0.1520933abs(MCE$coefficients[3])## res3_1
## 0.1520933Primero hacemos un modelo donde la variable dependiente es PCE y las variables independientes son GDP y Residuales y obtenemos un resumen del modelo anteriormente planteado y podemos observar que el incercepto tiene un nivel de significancia al 99.99% al igual que GDP, solo los residuales tiene un nivel de significacia al 90%, el nivel que explican las variables independientes a la dependiente es del 47.42%.
El coeficiente es tiene que ser negativo y el valor absoluto menor a 1 y si lo es, porque es -0.1520933 es negativo y también en valor absoluto sigue siendo menor que 1.