Series de Tiempo y Modelación de datos
Grupo 6
13 de septiembre del 2020
Trabajo Final del primer modulo del Programa de Especialización de Econometría Aplicada (X Edición) de la Universidad Nacional de Ingeniería.
Este trabajo fue resuelto de manera conjunto, del cual estaba conformada por:
- Quispe Duran, Edmar (edmar.qd97@gmail.com)
- Reyna Motta, Diana Milagros (dreyna2401@gmail.com)
- Serpa Tone, Williams Miguel (williams.tone.serpa@gmail.com)
- Vera Sánchez, Humberto Jesús (hjveras@unac.edu.pe)
- Zúñiga Franco, Jorge Albrecht (jazunigaf@gmail.com)
En esta oportunidad mostraremos la funciones de los paquetes tseries, urca, uroot y var a través de 2 casos prácticos.
Instalación de paquetes
Para la instalación de los paquetes que utilizaremos en este trabajo lo haremos con el comando install.packages() y el llamado correspondiente de los mimos lo haremos con el comando library().
# Instalación de paquetes
library(dygraphs)
library(quantmod)
library(ggfortify)
library(tseries)
library(PerformanceAnalytics)
library(forecast)
library(printr)
library(urca)
library(uroot)Paquete tseries
El paquete tseries nos permitirá manipular datos correspondiente a series temporales. Una de sus tantas funciones es el poder importar datos de activos financieros desde el mismo Yahoo Finance con el comando getSymbols.yahoo().
Para este trabajo importaremos 6 activos financieros que son : IBM, ALIBABA GROUP HOLDING LIMITED , AMAZON, FACEBOOK, MICROSOFT Y TESLA
Precios
Para este trabajo importaremos 6 activos financieros que son : IBM, ALIBABA GROUP HOLDING LIMITED , AMAZON, FACEBOOK, MICROSOFT Y TESLA
#===========================================================================================
# PRECIOS
#===========================================================================================
tickers=c('IBM','BABA','AMZN','FB','MSFT','TSLA')
precios=NULL
fecha='2015-01-01'
for(a in tickers){
precios<-cbind(precios,getSymbols.yahoo(a,from = fecha ,periodicity='daily',auto.assign=F)[,6])
}
cartera=merge(precios,all=F)
names(cartera)=c('IBM','BABA','AMZN','FB','MSFT','TSLA')
cartera=as.data.frame(cartera)
head(cartera, n=25)| IBM | BABA | AMZN | FB | MSFT | TSLA | |
|---|---|---|---|---|---|---|
| 2015-01-02 | 125.8829 | 103.60 | 308.52 | 78.45 | 41.64789 | 43.862 |
| 2015-01-05 | 123.9022 | 101.00 | 302.19 | 77.19 | 41.26491 | 42.018 |
| 2015-01-06 | 121.2301 | 103.32 | 295.29 | 76.15 | 40.65924 | 42.256 |
| 2015-01-07 | 120.4378 | 102.13 | 298.42 | 76.15 | 41.17583 | 42.190 |
| 2015-01-08 | 123.0555 | 105.03 | 300.46 | 78.18 | 42.38715 | 42.124 |
| 2015-01-09 | 123.5915 | 103.02 | 296.93 | 77.74 | 42.03088 | 41.332 |
| 2015-01-12 | 121.5175 | 101.62 | 291.41 | 76.72 | 41.50538 | 40.442 |
| 2015-01-13 | 121.8049 | 100.77 | 294.74 | 76.45 | 41.29162 | 40.850 |
| 2015-01-14 | 121.0204 | 99.58 | 293.27 | 76.28 | 40.93535 | 38.538 |
| 2015-01-15 | 120.0650 | 96.31 | 286.95 | 74.05 | 40.50784 | 38.374 |
| 2015-01-16 | 122.0612 | 96.89 | 290.74 | 75.18 | 41.18475 | 38.614 |
| 2015-01-20 | 121.9136 | 100.04 | 289.44 | 76.24 | 41.31834 | 38.386 |
| 2015-01-21 | 118.1386 | 103.29 | 297.25 | 76.74 | 40.89972 | 39.314 |
| 2015-01-22 | 120.7019 | 104.00 | 310.32 | 77.65 | 41.97744 | 40.324 |
| 2015-01-23 | 121.0747 | 103.11 | 312.39 | 77.83 | 42.02197 | 40.258 |
| 2015-01-26 | 121.4554 | 103.99 | 309.66 | 77.50 | 41.87055 | 41.310 |
| 2015-01-27 | 119.3659 | 102.94 | 306.75 | 75.78 | 37.99613 | 41.196 |
| 2015-01-28 | 117.7191 | 98.45 | 303.91 | 76.24 | 36.68684 | 39.874 |
| 2015-01-29 | 120.7718 | 89.81 | 311.78 | 78.00 | 37.41719 | 41.040 |
| 2015-01-30 | 119.0862 | 89.08 | 354.53 | 75.91 | 35.98321 | 40.720 |
| 2015-02-02 | 120.1349 | 90.13 | 364.47 | 74.99 | 36.76700 | 42.188 |
| 2015-02-03 | 123.0943 | 90.61 | 363.55 | 75.40 | 37.05203 | 43.672 |
| 2015-02-04 | 121.9214 | 90.00 | 364.75 | 75.63 | 37.26578 | 43.710 |
| 2015-02-05 | 122.6594 | 87.00 | 373.89 | 75.61 | 37.80909 | 44.198 |
| 2015-02-06 | 122.5890 | 85.68 | 374.28 | 74.47 | 37.77346 | 43.472 |
Retornos
Coeficiente de Determinación (\(R_{t}\)):
\[ R_{t}=\frac{\left({P}_{t}-{P}_{t-1}\right)}{{P}_{t-1}} \]
donde
\(R_{t}\)= Retorno Arimetico tiempo discreto.
\(P_{t}\)= Precio de cierre año base.
\(P_{t-1}\)= Precio de cierre año rezagado.
Gracias al paquete PerformanceAnalytics utilizaremos el comando Return.calculate() que nos permitirá hallar los retornos de cada unos de los 6 activos.
#===========================================================================================
# RETORNOS
#===========================================================================================
rendimiento=Return.calculate(cartera) # Similiar al diff(log())
rendimiento=rendimiento[-1,] # Al perder una observación elimamos el NA correspondiente a la primera fila
names(rendimiento)=c('R.IBM','R.BABA','R.AMZN','R.FB','R.MSFT','R.TSLA')
head(rendimiento, n=25)| R.IBM | R.BABA | R.AMZN | R.FB | R.MSFT | R.TSLA | |
|---|---|---|---|---|---|---|
| 2015-01-05 | -0.0157349 | -0.0250965 | -0.0205173 | -0.0160611 | -0.0091958 | -0.0420409 |
| 2015-01-06 | -0.0215659 | 0.0229703 | -0.0228333 | -0.0134732 | -0.0146774 | 0.0056642 |
| 2015-01-07 | -0.0065354 | -0.0115176 | 0.0105998 | 0.0000000 | 0.0127053 | -0.0015620 |
| 2015-01-08 | 0.0217348 | 0.0283952 | 0.0068359 | 0.0266579 | 0.0294181 | -0.0015643 |
| 2015-01-09 | 0.0043555 | -0.0191374 | -0.0117486 | -0.0056281 | -0.0084051 | -0.0188016 |
| 2015-01-12 | -0.0167807 | -0.0135895 | -0.0185902 | -0.0131206 | -0.0125026 | -0.0215330 |
| 2015-01-13 | 0.0023650 | -0.0083646 | 0.0114272 | -0.0035193 | -0.0051503 | 0.0100884 |
| 2015-01-14 | -0.0064408 | -0.0118090 | -0.0049875 | -0.0022236 | -0.0086280 | -0.0565973 |
| 2015-01-15 | -0.0078947 | -0.0328380 | -0.0215500 | -0.0292343 | -0.0104436 | -0.0042555 |
| 2015-01-16 | 0.0166264 | 0.0060222 | 0.0132078 | 0.0152599 | 0.0167106 | 0.0062542 |
| 2015-01-20 | -0.0012090 | 0.0325111 | -0.0044713 | 0.0140995 | 0.0032437 | -0.0059045 |
| 2015-01-21 | -0.0309652 | 0.0324870 | 0.0269831 | 0.0065582 | -0.0101315 | 0.0241754 |
| 2015-01-22 | 0.0216978 | 0.0068738 | 0.0439697 | 0.0118583 | 0.0263503 | 0.0256906 |
| 2015-01-23 | 0.0030889 | -0.0085577 | 0.0066706 | 0.0023181 | 0.0010609 | -0.0016368 |
| 2015-01-26 | 0.0031436 | 0.0085345 | -0.0087391 | -0.0042400 | -0.0036035 | 0.0261315 |
| 2015-01-27 | -0.0172039 | -0.0100971 | -0.0093974 | -0.0221936 | -0.0925332 | -0.0027597 |
| 2015-01-28 | -0.0137956 | -0.0436177 | -0.0092583 | 0.0060702 | -0.0344586 | -0.0320904 |
| 2015-01-29 | 0.0259321 | -0.0877603 | 0.0258958 | 0.0230850 | 0.0199078 | 0.0292421 |
| 2015-01-30 | -0.0139571 | -0.0081282 | 0.1371159 | -0.0267948 | -0.0383243 | -0.0077973 |
| 2015-02-02 | 0.0088058 | 0.0117871 | 0.0280371 | -0.0121197 | 0.0217822 | 0.0360511 |
| 2015-02-03 | 0.0246345 | 0.0053257 | -0.0025242 | 0.0054674 | 0.0077521 | 0.0351759 |
| 2015-02-04 | -0.0095283 | -0.0067322 | 0.0033008 | 0.0030503 | 0.0057690 | 0.0008701 |
| 2015-02-05 | 0.0060524 | -0.0333333 | 0.0250583 | -0.0002644 | 0.0145795 | 0.0111646 |
| 2015-02-06 | -0.0005740 | -0.0151724 | 0.0010430 | -0.0150774 | -0.0009425 | -0.0164261 |
| 2015-02-09 | -0.0061895 | 0.0037348 | -0.0099391 | -0.0004028 | -0.0011789 | 0.0005520 |
Gráficos de la Cartera como sus Retornos
Utilizaremos el comando dygraph() para crear un gráfico dinámico que nos mostrará el precio ajustado de cada acción como sus retornos a lo largo de los años.
#===========================================================================================
# GRÁFICOS DE PRECIOS
#===========================================================================================
color=c('red','green','blue','skyblue','brown','green"')
dygraph(cartera,main = 'EVOLUCIÓN DE CARTERA')%>%dyRangeSelector()%>%dyOptions(colors = color ,fillGraph = T)#===========================================================================================
# GRÁFICOS DE RENDIMIENTOS
#===========================================================================================
color2<-c("#F4FA58","#B40404","#2E9AFE","#FE2EF7","red","#00FFFF")
dygraph(rendimiento,main = 'RENDIMIENTO CARTERA')%>%dyRangeSelector()%>%dyOptions(colors = color2,fillGraph = T)Paquete urca (Test de Raíz Unitaria)
Debido a que instalamos el paquete urca este nos permitira hacer distintas pruebas econométricas como en este caso el test de Raíz Unitaria.
\[ Y_{t}={c}+\theta{Y}_{t-1}+\epsilon_{t} \]
Realizamos el siguiente contraste:
(\(H_{0}\)): \(\theta\) = 1.
(\(H_{1}\)): \(\theta\) < 1.
Los resultados indican si:
RECHAZAMOS \(H_{0}\) = La serie es estacionaria.
NO RECHAZAMOS \(H_{0}\) = La serie es Random Walk
El estadistico de la prueba es: \[t=\frac{\widehat{\theta}-1}{s.d(\widehat{\theta})}\]
Raíz Unitaria
Sea:
\[ Y_{t}=\theta_{1}{Y}_{t-1}+\epsilon_{t} \]
\[ Y_{t}={Y}_{t-1}+\epsilon_{t} \] \[ Y_{t}-{Y}_{t-1}=\epsilon_{t} \]
Operador de rezagos \[ \text{L}^{k}\text{Y}_{t}=\text{Y}_{t-k} \] \[ Y_{t}(1- \text{L})=\epsilon_{t} \] \[ 1- \text{L}=\theta(L)= \text{Polinomio Característico} \] \[ 1- \text{L}=0 \] \[ \text{L}=1\longrightarrow\text{La raíz de este polinomio es 1: Raíz Unitaria} \]
Cartera
#===============================================================================================================
#Test de Raíz Unitaria Dickey Fuller
#===============================================================================================================
# Analizamos el comportamiento de los precios de los activos para cada empresa
# haciendo uso de la librería "urca".
j=6 #j=6 debido a que son 6 precios asociados a cada empresa
# ur.df = Test de Raíz Unitaria Dickey Fuller
# Ho: La serie tiene raíz unitaria
for(i in 1:j){
print(summary(ur.df(cartera[,i], type = "drift", lags = 1)))
}##
## ###############################################
## # 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
## -15.3583 -0.8179 0.0951 0.9104 11.3014
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.938054 0.610698 3.174 0.00154 **
## z.lag.1 -0.015164 0.004757 -3.188 0.00147 **
## z.diff.lag -0.059889 0.026401 -2.268 0.02345 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.905 on 1429 degrees of freedom
## Multiple R-squared: 0.01159, Adjusted R-squared: 0.01021
## F-statistic: 8.38 on 2 and 1429 DF, p-value: 0.0002408
##
##
## Value of test-statistic is: -3.1876 5.081
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -15.536 -1.510 -0.050 1.533 21.171
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.288e-01 2.424e-01 0.531 0.595
## z.lag.1 -9.235e-05 1.590e-03 -0.058 0.954
## z.diff.lag 3.091e-02 2.649e-02 1.167 0.244
##
## Residual standard error: 3.199 on 1429 degrees of freedom
## Multiple R-squared: 0.0009516, Adjusted R-squared: -0.0004467
## F-statistic: 0.6806 on 2 and 1429 DF, p-value: 0.5065
##
##
## Value of test-statistic is: -0.0581 0.9359
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -183.838 -8.449 -0.049 9.667 228.164
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.755129 1.645964 0.459 0.64646
## z.lag.1 0.001061 0.001134 0.935 0.34969
## z.diff.lag -0.074060 0.026474 -2.797 0.00522 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.52 on 1429 degrees of freedom
## Multiple R-squared: 0.005836, Adjusted R-squared: 0.004444
## F-statistic: 4.194 on 2 and 1429 DF, p-value: 0.01527
##
##
## Value of test-statistic is: 0.9355 4.0779
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -41.119 -1.164 0.022 1.410 23.714
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.327838 0.312309 1.050 0.2940
## z.lag.1 -0.001228 0.001968 -0.624 0.5327
## z.diff.lag -0.064344 0.026435 -2.434 0.0151 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.346 on 1429 degrees of freedom
## Multiple R-squared: 0.00453, Adjusted R-squared: 0.003137
## F-statistic: 3.252 on 2 and 1429 DF, p-value: 0.039
##
##
## Value of test-statistic is: -0.6241 1.4628
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -17.3040 -0.4938 -0.0148 0.6478 14.8519
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.015276 0.116236 0.131 0.895
## z.lag.1 0.001486 0.001140 1.303 0.193
## z.diff.lag -0.317007 0.025141 -12.609 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.023 on 1429 degrees of freedom
## Multiple R-squared: 0.1003, Adjusted R-squared: 0.09903
## F-statistic: 79.64 on 2 and 1429 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: 1.3028 4.7559
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -89.489 -0.933 -0.053 0.861 52.500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.207019 0.210260 -0.985 0.324996
## z.lag.1 0.006440 0.002279 2.826 0.004784 **
## z.diff.lag -0.097855 0.026563 -3.684 0.000238 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.066 on 1429 degrees of freedom
## Multiple R-squared: 0.01307, Adjusted R-squared: 0.01169
## F-statistic: 9.46 on 2 and 1429 DF, p-value: 8.29e-05
##
##
## Value of test-statistic is: 2.8257 5.7437
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78Precio IBM: Si el t calculado cae por debajo del t critico no es más negativo que los demás valores rechazamos la Ho de que exista raíz unitaria.
En el caso analizado, vemos que el t calculado es más negativo que los t críticos, entonces se rechaza la Ho al 5% y 10% de significancia; y se afirma que la serie no tiene raíz unitaria.
Sin embargo al 1% de significancia existiría raíz unitaria.
Precio BABA: Se observa que el t calculado el cuál no es más negativo que los t críticos, entonces no se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie tiene raíz unitaria.
Precio AMZN: Se observa que el t calculado el cuál no es más negativo que los t críticos, entonces no se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie tiene raíz unitaria.
Precio FB: Se observa que el t calculado el cuál no es más negativo que los t críticos, entonces no se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie tiene raíz unitaria.
Precio MFST: Se observa que el t calculado el cuál no es más negativo que los t críticos, entonces no se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie tiene raíz unitaria.
Precio TSLA: Se observa que el t calculado el cuál no es más negativo que los t críticos, entonces no se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie tiene raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria Elliot Rotemberg y Stock (Dickey Fuller-GLS)
#===============================================================================================================
# ur.ers = Test de Raíz Unitaria Elliot Rotemberg y Stock (Dickey Fuller-GLS)
# Ho: La serie tiene raíz unitaria
for(i in 1:j){
print(summary(ur.ers(cartera[,i], type = "DF-GLS", model = "constant",lag.max = 1)))
}##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.3263 -0.7880 0.1208 0.9403 11.3289
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag -0.014674 0.004673 -3.14 0.00172 **
## yd.diff.lag1 -0.060165 0.026390 -2.28 0.02277 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.905 on 1430 degrees of freedom
## Multiple R-squared: 0.01138, Adjusted R-squared: 0.009998
## F-statistic: 8.231 on 2 and 1430 DF, p-value: 0.0002791
##
##
## Value of test-statistic is: -3.14
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.5085 -1.4196 0.0593 1.6179 21.1521
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag 0.0009582 0.0013035 0.735 0.462
## yd.diff.lag1 0.0307766 0.0264969 1.162 0.246
##
## Residual standard error: 3.199 on 1430 degrees of freedom
## Multiple R-squared: 0.001408, Adjusted R-squared: 1.124e-05
## F-statistic: 1.008 on 2 and 1430 DF, p-value: 0.3652
##
##
## Value of test-statistic is: 0.7351
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -184.344 -7.705 0.558 9.862 227.233
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag 0.0018469 0.0006785 2.722 0.00657 **
## yd.diff.lag1 -0.0743623 0.0264692 -2.809 0.00503 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.52 on 1430 degrees of freedom
## Multiple R-squared: 0.009686, Adjusted R-squared: 0.008301
## F-statistic: 6.993 on 2 and 1430 DF, p-value: 0.0009498
##
##
## Value of test-statistic is: 2.7219
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.200 -1.097 0.112 1.471 23.493
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag 0.001066 0.001059 1.006 0.3146
## yd.diff.lag1 -0.065284 0.026435 -2.470 0.0136 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.347 on 1430 degrees of freedom
## Multiple R-squared: 0.00475, Adjusted R-squared: 0.003358
## F-statistic: 3.412 on 2 and 1430 DF, p-value: 0.03324
##
##
## Value of test-statistic is: 1.006
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.3189 -0.4448 0.0500 0.6981 14.8498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag 0.0023450 0.0008109 2.892 0.00389 **
## yd.diff.lag1 -0.3171257 0.0251425 -12.613 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.023 on 1430 degrees of freedom
## Multiple R-squared: 0.1021, Adjusted R-squared: 0.1009
## F-statistic: 81.32 on 2 and 1430 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: 2.8918
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -89.602 -0.850 0.032 0.949 52.370
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag 0.006996 0.002100 3.331 0.000886 ***
## yd.diff.lag1 -0.098117 0.026554 -3.695 0.000228 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.065 on 1430 degrees of freedom
## Multiple R-squared: 0.01482, Adjusted R-squared: 0.01344
## F-statistic: 10.76 on 2 and 1430 DF, p-value: 2.311e-05
##
##
## Value of test-statistic is: 3.3313
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62Precio IBM: Se observa que el tcalculado es más negativo que los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio BABA: Se observa que el tcalculado es positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio AMZN: Se observa que el tcalculado es positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio FB: Se observa que el tcalculado es positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio MFST: Se observa que el tcalculado es positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio TSLA: Se observa que el tcalculado es positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria Elliot Rotemberg y Stock (Punto Óptimo)
#===============================================================================================================
# ur.ers = Test de Raíz Unitaria Elliot Rotemberg y Stock (Punto Óptimo)
# Ho: La serie tiene raíz unitaria
for(i in 1:j){
print(summary(ur.ers(cartera[,i], type = "P-test", model = "constant",lag.max = 1)))
}##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 1.2657
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 25.972
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 112.2283
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 42.1521
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 118.6121
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 31.3699
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48Precio IBM: Se observa que el tcalculado es menos positivo que los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio BABA: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio AMZN: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio FB: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio MFST: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio TSLA: Se observa que el tcalculado es positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria de Kwiatkowski
#===============================================================================================================
# ur.kpss = Test de Raíz Unitaria de Kwiatkowski
# Ho: La series es estacionaria.
for(i in 1:j){
print(summary(ur.kpss(cartera[,i], type = "tau", lags = "short")))
}##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 1.0005
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.9571
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.8976
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.8682
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 3.2813
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 1.4408
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216Precio IBM: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que existe raíz unitaria.
Precio BABA: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que existe raíz unitaria.
Precio AMZN: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que existe raíz unitaria.
Precio FB: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que existe raíz unitaria.
Precio MFST: Se observa que el tcalculado es más positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que existe raíz unitaria.
Precio TSLA: Se observa que el tcalculado es positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que existe raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria Phillip Perron
#===============================================================================================================
# ur.pp = Test de Raíz Unitaria Phillip Perron
# Ho: La serie tiene raíz unitaria
for(i in 1:j){
print(summary(ur.pp(cartera[,i], type = "Z-tau", model = "constant")))
}##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.9729 -0.8142 0.1053 0.9254 11.3175
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.059190 0.609063 3.381 0.000742 ***
## y.l1 0.983879 0.004745 207.367 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.908 on 1431 degrees of freedom
## Multiple R-squared: 0.9678, Adjusted R-squared: 0.9678
## F-statistic: 4.3e+04 on 1 and 1431 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic, type: Z-tau is: -3.3701
##
## aux. Z statistics
## Z-tau-mu 3.3534
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437701 -2.864015 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.2694 -1.5295 -0.0351 1.5910 21.0487
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.111118 0.242047 0.459 0.646
## y.l1 1.000043 0.001587 630.216 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.199 on 1431 degrees of freedom
## Multiple R-squared: 0.9964, Adjusted R-squared: 0.9964
## F-statistic: 3.972e+05 on 1 and 1431 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic, type: Z-tau is: 0.0727
##
## aux. Z statistics
## Z-tau-mu 0.426
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437701 -2.864015 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -190.946 -8.425 -0.277 9.340 231.465
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.859700 1.647065 0.522 0.602
## y.l1 1.000859 0.001133 883.326 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.59 on 1431 degrees of freedom
## Multiple R-squared: 0.9982, Adjusted R-squared: 0.9982
## F-statistic: 7.803e+05 on 1 and 1431 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic, type: Z-tau is: 0.8586
##
## aux. Z statistics
## Z-tau-mu 0.4846
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437701 -2.864015 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.276 -1.185 -0.018 1.377 23.146
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.353091 0.312104 1.131 0.258
## y.l1 0.998543 0.001966 507.956 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.351 on 1431 degrees of freedom
## Multiple R-squared: 0.9945, Adjusted R-squared: 0.9945
## F-statistic: 2.58e+05 on 1 and 1431 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic, type: Z-tau is: -0.609
##
## aux. Z statistics
## Z-tau-mu 1.0327
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437701 -2.864015 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23.4442 -0.5232 -0.0340 0.6258 19.5244
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.056659 0.122315 0.463 0.643
## y.l1 1.000625 0.001199 834.732 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.131 on 1431 degrees of freedom
## Multiple R-squared: 0.998, Adjusted R-squared: 0.9979
## F-statistic: 6.968e+05 on 1 and 1431 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic, type: Z-tau is: 1.1219
##
## aux. Z statistics
## Z-tau-mu 0.2029
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437701 -2.864015 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -90.152 -0.921 -0.096 0.843 53.471
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.143926 0.210297 -0.684 0.494
## y.l1 1.005226 0.002264 444.021 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.087 on 1431 degrees of freedom
## Multiple R-squared: 0.9928, Adjusted R-squared: 0.9928
## F-statistic: 1.972e+05 on 1 and 1431 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic, type: Z-tau is: 2.2163
##
## aux. Z statistics
## Z-tau-mu -0.6318
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437701 -2.864015 -2.568106Precio IBM: Se observa que el ztau es más negativo que los zcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio BABA: Se observa que el ztau es menos negativos comparado con los zcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio AMZN: Se observa que el ztau es positivo comparado con los zcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio FB: Se observa que el ztau es menos negativo comparado con los zcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio MFST: Se observa que el ztau es positivo comparado con los zcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
Precio TSLA: Se observa que el ztau es positivo comparado con los zcriticos entonces no se rechaza la Ho y se afirma que existe raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria con Quiebre estructural de Zivot & Andrews
#===============================================================================================================
#ur.za = Test de Raíz Unitaria con Quiebre estructural de Zivot & Andrews
for(i in 1:j){
print(summary(ur.za(cartera[,i])))
}##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.9629 -0.8187 0.0837 0.9243 11.1557
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.0647452 0.7076968 4.331 1.59e-05 ***
## y.l1 0.9752387 0.0056561 172.421 < 2e-16 ***
## trend -0.0004688 0.0002056 -2.280 0.02276 *
## du 0.5900163 0.2104410 2.804 0.00512 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.904 on 1429 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.968, Adjusted R-squared: 0.9679
## F-statistic: 1.44e+04 on 3 and 1429 DF, p-value: < 2.2e-16
##
##
## Teststatistic: -4.3778
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 374
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.6267 -1.4538 -0.0808 1.5489 21.0805
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4511956 0.2734754 1.650 0.09919 .
## y.l1 0.9852100 0.0040165 245.289 < 2e-16 ***
## trend 0.0030568 0.0007237 4.224 2.55e-05 ***
## du -1.1066256 0.3559140 -3.109 0.00191 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.181 on 1429 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9965, Adjusted R-squared: 0.9964
## F-statistic: 1.339e+05 on 3 and 1429 DF, p-value: < 2.2e-16
##
##
## Teststatistic: -3.6823
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 897
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -203.824 -8.571 -0.521 9.656 227.514
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.317375 1.919532 3.291 0.00102 **
## y.l1 0.979454 0.004462 219.534 < 2e-16 ***
## trend 0.028100 0.006555 4.287 1.93e-05 ***
## du 22.666170 4.264400 5.315 1.23e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.28 on 1429 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9982, Adjusted R-squared: 0.9982
## F-statistic: 2.655e+05 on 3 and 1429 DF, p-value: < 2.2e-16
##
##
## Teststatistic: -4.6051
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 1323
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39.081 -1.119 0.047 1.381 24.572
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.9456743 0.4532491 4.293 1.88e-05 ***
## y.l1 0.9689570 0.0060642 159.784 < 2e-16 ***
## trend 0.0050324 0.0009478 5.310 1.27e-07 ***
## du -1.8717380 0.4270807 -4.383 1.26e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.321 on 1429 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9946, Adjusted R-squared: 0.9946
## F-statistic: 8.759e+04 on 3 and 1429 DF, p-value: < 2.2e-16
##
##
## Teststatistic: -5.1191
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 897
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.9649 -0.5606 -0.0051 0.6224 19.4759
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.5725232 0.1529740 3.743 0.000189 ***
## y.l1 0.9736678 0.0049782 195.587 < 2e-16 ***
## trend 0.0024938 0.0004895 5.095 3.96e-07 ***
## du 1.6178199 0.3147312 5.140 3.12e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.108 on 1429 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.998, Adjusted R-squared: 0.998
## F-statistic: 2.375e+05 on 3 and 1429 DF, p-value: < 2.2e-16
##
##
## Teststatistic: -5.2895
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 1314
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -89.577 -1.047 -0.059 0.846 54.715
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.5619821 0.3139766 1.790 0.07368 .
## y.l1 0.9780228 0.0050353 194.233 < 2e-16 ***
## trend 0.0012997 0.0004042 3.215 0.00133 **
## du 8.2386047 1.4011204 5.880 5.1e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.026 on 1429 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.993, Adjusted R-squared: 0.993
## F-statistic: 6.732e+04 on 3 and 1429 DF, p-value: < 2.2e-16
##
##
## Teststatistic: -4.3646
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 1381Al analizar las series de los precios de las acciones se observa que la serie presenta raíz unitaria en todos los precios de acciones.
Rendimientos
#===============================================================================================================
#Test de Raíz Unitaria Dickey Fuller
#===============================================================================================================
# Analizamos el comportamiento de los rendimientos de los activos para cada empresa
# haciendo uso de la librería "urca".
j=6 #j=6 debido a que son 6 los rendimientos asociados a los activos de cada empresa
# ur.df = Test de Raíz Unitaria Dickey Fuller
# Ho: La serie tiene raíz unitaria
for(i in 1:j){
print(summary(ur.df(rendimiento[,i], type = "drift", lags = 1)))
}##
## ###############################################
## # 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
## -0.136079 -0.006586 0.000423 0.006863 0.114637
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0001294 0.0004134 0.313 0.7544
## z.lag.1 -1.0388461 0.0389750 -26.654 <2e-16 ***
## z.diff.lag -0.0468878 0.0264129 -1.775 0.0761 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01564 on 1428 degrees of freedom
## Multiple R-squared: 0.5462, Adjusted R-squared: 0.5456
## F-statistic: 859.5 on 2 and 1428 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -26.6542 355.2243
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -0.087137 -0.011984 -0.000203 0.011458 0.131484
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0008810 0.0005465 1.612 0.107
## z.lag.1 -0.9920940 0.0366215 -27.090 <2e-16 ***
## z.diff.lag 0.0345754 0.0264356 1.308 0.191
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02064 on 1428 degrees of freedom
## Multiple R-squared: 0.4802, Adjusted R-squared: 0.4795
## F-statistic: 659.6 on 2 and 1428 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -27.0905 366.9467
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -0.081899 -0.008742 -0.000265 0.008707 0.139427
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0018861 0.0005175 3.645 0.000277 ***
## z.lag.1 -1.0284595 0.0378969 -27.138 < 2e-16 ***
## z.diff.lag 0.0031264 0.0264685 0.118 0.905990
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0194 on 1428 degrees of freedom
## Multiple R-squared: 0.5127, Adjusted R-squared: 0.512
## F-statistic: 751.3 on 2 and 1428 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -27.1384 368.2454
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -0.189989 -0.008153 0.000115 0.009886 0.152113
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0011389 0.0005265 2.163 0.0307 *
## z.lag.1 -1.0596482 0.0386290 -27.431 <2e-16 ***
## z.diff.lag -0.0057966 0.0264622 -0.219 0.8266
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01986 on 1428 degrees of freedom
## Multiple R-squared: 0.533, Adjusted R-squared: 0.5323
## F-statistic: 814.9 on 2 and 1428 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -27.4314 376.2405
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -0.118585 -0.006622 -0.000163 0.007840 0.118967
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0015817 0.0004569 3.462 0.000553 ***
## z.lag.1 -1.2344627 0.0413379 -29.863 < 2e-16 ***
## z.diff.lag 0.0124295 0.0264791 0.469 0.638848
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01717 on 1428 degrees of freedom
## Multiple R-squared: 0.6098, Adjusted R-squared: 0.6093
## F-statistic: 1116 on 2 and 1428 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -29.8628 445.892
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
##
##
## ###############################################
## # 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
## -0.208374 -0.015797 -0.001357 0.015453 0.191843
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0019995 0.0009118 2.193 0.0285 *
## z.lag.1 -0.9458162 0.0372655 -25.381 <2e-16 ***
## z.diff.lag -0.0487985 0.0264170 -1.847 0.0649 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03436 on 1428 degrees of freedom
## Multiple R-squared: 0.4984, Adjusted R-squared: 0.4977
## F-statistic: 709.4 on 2 and 1428 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -25.3805 322.0852
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78Precio IBM: Si el t calculado cae por debajo del t critico o es más negativo que los demás valores rechazamos la Ho de que exista raíz unitaria.
En el caso analizado, vemos que el t calculado es más negativo que los t críticos, entonces se rechaza la Ho; y se afirma que la serie no tiene raíz unitaria.
Precio BABA: Se observa que el t calculado el cuál es más negativo que los t críticos, entonces se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie no tiene raíz unitaria.
Precio AMZN: Se observa que el t calculado el cuál es más negativo que los t críticos, entonces se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie no tiene raíz unitaria.
Precio FB: Se observa que el t calculado el cuál es más negativo que los t críticos, entonces se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie no tiene raíz unitaria.
Precio MFST: Se observa que el t calculado el cuál es más negativo que los t críticos, entonces se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie no tiene raíz unitaria.
Precio TSLA: Se observa que el t calculado el cuál es más negativo que los t críticos, entonces se rechaza la Ho en todos los niveles de significancia; y se afirma que la serie no tiene raíz unitaria.
#===============================================================================================================
#Test Raíz Unitaria Elliot Rotemberg y Stock (Dickey Fuller-GLS)
#===============================================================================================================
# ur.ers = Test de Raíz Unitaria Elliot Rotemberg y Stock (Dickey Fuller-GLS)
# Ho: La serie tiene raíz unitaria
for(i in 1:j){
print(summary(ur.ers(rendimiento[,i], type = "DF-GLS", model = "constant",lag.max = 1)))
}##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.132427 -0.002757 0.005205 0.012892 0.139421
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag -0.33904 0.02576 -13.16 <2e-16 ***
## yd.diff.lag1 -0.39676 0.02429 -16.33 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01807 on 1429 degrees of freedom
## Multiple R-squared: 0.394, Adjusted R-squared: 0.3931
## F-statistic: 464.5 on 2 and 1429 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -13.1624
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.074738 -0.007198 0.005743 0.019992 0.137834
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag -0.26096 0.02204 -11.84 <2e-16 ***
## yd.diff.lag1 -0.33090 0.02495 -13.26 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02422 on 1429 degrees of freedom
## Multiple R-squared: 0.2834, Adjusted R-squared: 0.2824
## F-statistic: 282.5 on 2 and 1429 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -11.8398
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.094206 -0.004259 0.005347 0.016429 0.148165
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag -0.28978 0.02354 -12.31 <2e-16 ***
## yd.diff.lag1 -0.36640 0.02462 -14.88 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0227 on 1429 degrees of freedom
## Multiple R-squared: 0.3322, Adjusted R-squared: 0.3313
## F-statistic: 355.5 on 2 and 1429 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -12.3096
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.192046 -0.003170 0.006528 0.017544 0.168162
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag -0.42758 0.02813 -15.20 <2e-16 ***
## yd.diff.lag1 -0.32190 0.02505 -12.85 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02276 on 1429 degrees of freedom
## Multiple R-squared: 0.3862, Adjusted R-squared: 0.3853
## F-statistic: 449.5 on 2 and 1429 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -15.2019
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.124448 -0.000956 0.006397 0.014765 0.166162
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag -0.66744 0.03447 -19.36 <2e-16 ***
## yd.diff.lag1 -0.27140 0.02547 -10.66 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01947 on 1429 degrees of freedom
## Multiple R-squared: 0.4979, Adjusted R-squared: 0.4972
## F-statistic: 708.6 on 2 and 1429 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -19.3655
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type DF-GLS
## detrending of series with intercept
##
##
## Call:
## lm(formula = dfgls.form, data = data.dfgls)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.292369 -0.009742 0.008596 0.029246 0.264813
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## yd.lag -0.23413 0.02147 -10.91 <2e-16 ***
## yd.diff.lag1 -0.40428 0.02419 -16.71 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03976 on 1429 degrees of freedom
## Multiple R-squared: 0.328, Adjusted R-squared: 0.3271
## F-statistic: 348.8 on 2 and 1429 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -10.9064
##
## Critical values of DF-GLS are:
## 1pct 5pct 10pct
## critical values -2.57 -1.94 -1.62Precio IBM: Se observa que el tcalculado es más negativo que los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio BABA: Se observa que el tcalculado es más negativo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio AMZN: Se observa que el tcalculado es más negativo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio FB: Se observa que el tcalculado es más negativo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio MFST: Se observa que el tcalculado es más negativo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio TSLA: Se observa que el tcalculado es más negativo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria Elliot Rotemberg y Stock (Punto Óptimo)
#===============================================================================================================
# ur.ers = Test de Raíz Unitaria Elliot Rotemberg y Stock (Punto Óptimo)
# Ho: La serie tiene raíz unitaria
for(i in 1:j){
print(summary(ur.ers(rendimiento[,i], type = "P-test", model = "constant",lag.max = 1)))
}##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 0.0861
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 0.0972
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 0.0775
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 0.0607
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 0.047
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48
##
##
## ###############################################
## # Elliot, Rothenberg and Stock Unit Root Test #
## ###############################################
##
## Test of type P-test
## detrending of series with intercept
##
## Value of test-statistic is: 0.1064
##
## Critical values of P-test are:
## 1pct 5pct 10pct
## critical values 1.99 3.26 4.48Precio IBM: Se observa que el tcalculado es menos positivo que los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio BABA: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio AMZN: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio FB: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio MFST: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio TSLA: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria de Kwiatkowski
#===============================================================================================================
# ur.kpss = Test de Raíz Unitaria de Kwiatkowski
# Ho: La series es estacionaria.
for(i in 1:j){
print(summary(ur.kpss(rendimiento[,i], type = "tau", lags = "short")))
}##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.0208
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.0892
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.0536
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.0436
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.0143
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216
##
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: tau with 7 lags.
##
## Value of test-statistic is: 0.1479
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.119 0.146 0.176 0.216Precio IBM: Se observa que el tcalculado es menos positivo que los tcriticos entonces no se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio BABA: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio AMZN: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio FB: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces no se re0chaza la Ho y se afirma que no existe raíz unitaria.
Precio MFST: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio TSLA: Se observa que el tcalculado es menos positivo comparado con los tcriticos entonces no se rechaza la Ho y se afirma que no existe raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria Test Phillip Perron
#===============================================================================================================
# ur.pp = Test de Raíz Unitaria Phillip Perron
# Ho: La serie tiene raíz unitaria
for(i in 1:j){
print(summary(ur.pp(rendimiento[,i], type = "Z-tau", model = "constant")))
}##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.133468 -0.006479 0.000456 0.006985 0.112315
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0001184 0.0004137 0.286 0.77474
## y.l1 -0.0888541 0.0263323 -3.374 0.00076 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01566 on 1430 degrees of freedom
## Multiple R-squared: 0.007899, Adjusted R-squared: 0.007206
## F-statistic: 11.39 on 1 and 1430 DF, p-value: 0.0007597
##
##
## Value of test-statistic, type: Z-tau is: -41.2963
##
## aux. Z statistics
## Z-tau-mu 0.2859
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437704 -2.864016 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.086880 -0.011790 -0.000294 0.011352 0.131723
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0008685 0.0005460 1.591 0.112
## y.l1 0.0400919 0.0264128 1.518 0.129
##
## Residual standard error: 0.02064 on 1430 degrees of freedom
## Multiple R-squared: 0.001609, Adjusted R-squared: 0.0009104
## F-statistic: 2.304 on 1 and 1430 DF, p-value: 0.1293
##
##
## Value of test-statistic, type: Z-tau is: -36.3137
##
## aux. Z statistics
## Z-tau-mu 1.5895
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437704 -2.864016 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.081989 -0.008720 -0.000253 0.008731 0.139462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0018607 0.0005148 3.614 0.000312 ***
## y.l1 -0.0242071 0.0264345 -0.916 0.359958
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0194 on 1430 degrees of freedom
## Multiple R-squared: 0.0005861, Adjusted R-squared: -0.0001128
## F-statistic: 0.8386 on 1 and 1430 DF, p-value: 0.36
##
##
## Value of test-statistic, type: Z-tau is: -38.776
##
## aux. Z statistics
## Z-tau-mu 3.6173
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437704 -2.864016 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.189882 -0.008154 0.000131 0.009847 0.152140
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0011340 0.0005252 2.159 0.0310 *
## y.l1 -0.0653512 0.0263819 -2.477 0.0134 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01985 on 1430 degrees of freedom
## Multiple R-squared: 0.004273, Adjusted R-squared: 0.003576
## F-statistic: 6.136 on 1 and 1430 DF, p-value: 0.01336
##
##
## Value of test-statistic, type: Z-tau is: -40.5104
##
## aux. Z statistics
## Z-tau-mu 2.1659
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437704 -2.864016 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.117822 -0.006527 -0.000168 0.007794 0.119862
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0015489 0.0004547 3.406 0.000677 ***
## y.l1 -0.2188738 0.0258016 -8.483 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01716 on 1430 degrees of freedom
## Multiple R-squared: 0.04791, Adjusted R-squared: 0.04725
## F-statistic: 71.96 on 1 and 1430 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic, type: Z-tau is: -47.6535
##
## aux. Z statistics
## Z-tau-mu 3.4359
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437704 -2.864016 -2.568106
##
##
## ##################################
## # Phillips-Perron Unit Root Test #
## ##################################
##
## Test regression with intercept
##
##
## Call:
## lm(formula = y ~ y.l1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.212886 -0.015531 -0.001247 0.015375 0.196761
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0021030 0.0009102 2.31 0.021 *
## y.l1 0.0055572 0.0264287 0.21 0.833
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03438 on 1430 degrees of freedom
## Multiple R-squared: 3.092e-05, Adjusted R-squared: -0.0006684
## F-statistic: 0.04421 on 1 and 1430 DF, p-value: 0.8335
##
##
## Value of test-statistic, type: Z-tau is: -37.6529
##
## aux. Z statistics
## Z-tau-mu 2.312
##
## Critical values for Z statistics:
## 1pct 5pct 10pct
## critical values -3.437704 -2.864016 -2.568106Precio IBM: Se observa que el ztau es más negativo que los zcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio BABA: Se observa que el ztau es más negativo comparado con los zcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio AMZN: Se observa que el ztau es más negativo negativo comparado con los zcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio FB: Se observa que el ztau es más negativo comparado con los zcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio MFST: Se observa que el ztau es más negativo comparado con los zcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
Precio TSLA: Se observa que el ztau es más negativo comparado con los zcriticos entonces se rechaza la Ho y se afirma que no existe raíz unitaria.
#===============================================================================================================
#Test de Raíz Unitaria con Quiebre estructural de Zivot & Andrews
#===============================================================================================================
# ur.za = Test de Raíz Unitaria con Quiebre estructural de Zivot & Andrews
for(i in 1:j){
print(summary(ur.za(rendimiento[,i])))
}##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.132527 -0.006249 0.000646 0.006870 0.109508
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.533e-04 8.648e-04 0.871 0.383862
## y.l1 -9.207e-02 2.634e-02 -3.496 0.000487 ***
## trend -1.341e-06 1.140e-06 -1.177 0.239426
## du 3.913e-03 1.702e-03 2.299 0.021665 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01564 on 1428 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.01156, Adjusted R-squared: 0.009485
## F-statistic: 5.568 on 3 and 1428 DF, p-value: 0.0008491
##
##
## Teststatistic: -41.4618
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 1313
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08477 -0.01166 -0.00047 0.01125 0.13002
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.578e-03 1.255e-03 -1.258 0.20864
## y.l1 3.528e-02 2.643e-02 1.335 0.18213
## trend 6.844e-06 2.618e-06 2.614 0.00903 **
## du -5.328e-03 2.170e-03 -2.456 0.01418 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02061 on 1428 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.00647, Adjusted R-squared: 0.004383
## F-statistic: 3.1 on 3 and 1428 DF, p-value: 0.02588
##
##
## Teststatistic: -36.5014
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 772
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.082079 -0.008774 -0.000364 0.008695 0.139167
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.181e-03 1.028e-03 2.122 0.034 *
## y.l1 -2.864e-02 2.642e-02 -1.084 0.279
## trend -3.047e-07 1.245e-06 -0.245 0.807
## du -2.244e-02 7.981e-03 -2.811 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01935 on 1428 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.006305, Adjusted R-squared: 0.004217
## F-statistic: 3.02 on 3 and 1428 DF, p-value: 0.02883
##
##
## Teststatistic: -38.9305
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 1427
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.188927 -0.008125 0.000085 0.009852 0.151639
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.998e-03 1.097e-03 1.821 0.06886 .
## y.l1 -7.079e-02 2.639e-02 -2.683 0.00738 **
## trend -1.947e-06 1.448e-06 -1.344 0.17904
## du 6.280e-03 2.141e-03 2.933 0.00341 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0198 on 1428 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.01024, Adjusted R-squared: 0.008161
## F-statistic: 4.925 on 3 and 1428 DF, p-value: 0.002088
##
##
## Teststatistic: -40.5812
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 1310
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.117891 -0.006677 0.000017 0.007830 0.118087
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.898e-04 9.062e-04 0.540 0.588971
## y.l1 -2.261e-01 2.574e-02 -8.782 < 2e-16 ***
## trend 1.645e-06 1.099e-06 1.497 0.134710
## du -2.681e-02 7.048e-03 -3.804 0.000149 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01708 on 1428 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.05821, Adjusted R-squared: 0.05623
## F-statistic: 29.42 on 3 and 1428 DF, p-value: < 2.2e-16
##
##
## Teststatistic: -47.6248
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 1427
##
##
## ################################
## # Zivot-Andrews Unit Root Test #
## ################################
##
##
## Call:
## lm(formula = testmat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.225557 -0.015507 -0.000665 0.015846 0.197760
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.167e-04 1.892e-03 0.273 0.784808
## y.l1 -6.441e-03 2.642e-02 -0.244 0.807397
## trend 6.019e-07 2.499e-06 0.241 0.809700
## du 1.373e-02 3.699e-03 3.712 0.000214 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03418 on 1428 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.01327, Adjusted R-squared: 0.01119
## F-statistic: 6.399 on 3 and 1428 DF, p-value: 0.0002636
##
##
## Teststatistic: -38.1008
## Critical values: 0.01= -5.34 0.05= -4.8 0.1= -4.58
##
## Potential break point at position: 1310Al analizar las series de los rendimientos de las acciones se observa que la serie no presenta raíz unitaria en ninguno de los precios de las acciones, por lo que todas las series de rendimientos son estacionarias.
Paquete urca (Test de Cointegración)
El Test de Cointegración de Johansen indica como uno de los requisitos que deben cumplir las series es que sean integradas del mismo orden. En este caso solamente consideraremos a las series de precios debido a que presentan raíz unitaria; sin embargo a las series de rendimiento no se aplicará el test por ser estacionarias. Usando la librería urca, se tiene:
#===============================================================================================================
#Test de Cointegración
#===============================================================================================================
#ca.jo = Test de Cointegración de Johansen para los precios
BABAAdj = unclass(cartera$BABA)
IBMAdj = unclass(cartera$IBM)
AMZNAdj = unclass(cartera$AMZN)
FBAdj = unclass(cartera$FB)
MSFTdj = unclass(cartera$MSFT)
TSLAAdj = unclass(cartera$TSLA)
jotest_pr=ca.jo(data.frame(BABAAdj,IBMAdj,AMZNAdj,FBAdj,MSFTdj,TSLAAdj), type="trace", K=2,
ecdet="none", spec="longrun")
summary(jotest_pr)##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , with linear trend
##
## Eigenvalues (lambda):
## [1] 0.0195973688 0.0153883104 0.0086089489 0.0071101163 0.0051297394
## [6] 0.0003482763
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 5 | 0.50 6.50 8.18 11.65
## r <= 4 | 7.86 15.66 17.95 23.52
## r <= 3 | 18.08 28.71 31.52 37.22
## r <= 2 | 30.46 45.23 48.28 55.43
## r <= 1 | 52.67 66.49 70.60 78.87
## r = 0 | 81.01 85.18 90.39 104.20
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## BABAAdj.l2 IBMAdj.l2 AMZNAdj.l2 FBAdj.l2 MSFTdj.l2 TSLAAdj.l2
## BABAAdj.l2 1.00000000 1.0000000 1.0000000 1.00000000 1.0000000 1.0000000
## IBMAdj.l2 0.61645149 -8.8973950 -8.0204020 -3.28597416 0.7623394 -0.5031681
## AMZNAdj.l2 0.02369169 0.0168082 -0.2167507 -0.08945754 -0.2671506 0.1198567
## FBAdj.l2 -1.41858096 4.1802042 -0.1932058 -0.54343239 0.9341836 0.4963289
## MSFTdj.l2 -0.21927800 -4.6431671 -0.6577816 1.97365656 1.8358823 -3.1447266
## TSLAAdj.l2 -0.01582820 -2.1621370 2.1648082 -0.51591539 0.1483826 0.5077412
##
## Weights W:
## (This is the loading matrix)
##
## BABAAdj.l2 IBMAdj.l2 AMZNAdj.l2 FBAdj.l2 MSFTdj.l2
## BABAAdj.d -0.013032121 -8.224913e-05 0.0004838815 0.0009924962 -0.0002463108
## IBMAdj.d -0.002680791 8.505760e-04 0.0006013330 0.0015563783 -0.0009384173
## AMZNAdj.d 0.007229914 -1.802531e-03 0.0037624116 0.0333437911 0.0136960974
## FBAdj.d 0.007281273 -4.912392e-04 0.0005380989 0.0020631118 -0.0021242019
## MSFTdj.d -0.001679137 4.024108e-04 -0.0003735842 0.0021952796 -0.0005712446
## TSLAAdj.d -0.013178861 -2.147659e-03 -0.0005020665 0.0052818698 -0.0016353255
## TSLAAdj.l2
## BABAAdj.d -7.802865e-04
## IBMAdj.d -1.104711e-05
## AMZNAdj.d -4.909649e-03
## FBAdj.d -7.198497e-04
## MSFTdj.d -3.427212e-04
## TSLAAdj.d 1.835403e-04La primera sección muestra los valores propios generados por la prueba. En este caso tenemos seis valores correspondientes a los precios de las seis acciones.
La siguiente sección muestra el estadístico de prueba de trazas para las seis hipótesis. Para cada una de estas tres pruebas, no solo tenemos las estadística en sí, sino también los valores críticos en los niveles de confianza: 10%, 5% y 1% respectivamente.
Para la primera hipótesis (r=0), la estadística de prueba no supera significativamente a ningún nivel de confianza por lo que no se rechaza la hipótesis nula de no cointegración.
De igual modo, para las siguientes hipótesis desde (r<=1) hasta r(r<=5) no se rechaza la hipótesis nula de no cointegración.
Paquete uroot
Este paquete contiene varias funciones para analizar series de tiempo. Prueba de raíz unitaria: ADF, KPSS, HEGY, PP y CH, así como gráficos: Buys-Ballot y ciclos estacionales, entre otros, se han implementado para realizar un análisis analítico o gráfico. El uso combinado de ambos permite al usuario caracterizar la estacionalidad como determinista, estocástica o una mezcla de ellas.
Probamos la existencia de raíz unitaria con el paquete R UROOT usando la prueba de Phillips-Perron para la H0 de una raíz unitaria de una serie, es decir la serie de tiempo no estacionaria
pp.test(x, type = c(“Z_rho”, “Z_tau”), lag.short = TRUE, output = TRUE)
Argumentos
X: un vector numérico o una serie de tiempo univariante.
type: el tipo de prueba de Phillips-Perron. El valor predeterminado es Z_rho.
lag.short: un valor lógico que indica si el parámetro de retraso para calcular la estadística es a corto o largo plazo. El valor predeterminado es a corto plazo.
output: valor lógico que indica imprimir los resultados en la consola R. El valor predeterminado es TRUE.
Precios
#=======================================================================
#Prueba de Phillips-Perron
#=======================================================================
j=6
for (i in 1:j) {
print(pp.test(cartera[,i]))
}##
## Phillips-Perron Unit Root Test
##
## data: cartera[, i]
## Dickey-Fuller Z(alpha) = -22.713, Truncation lag parameter = 7, p-value
## = 0.04083
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: cartera[, i]
## Dickey-Fuller Z(alpha) = -13.021, Truncation lag parameter = 7, p-value
## = 0.3834
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: cartera[, i]
## Dickey-Fuller Z(alpha) = -6.9522, Truncation lag parameter = 7, p-value
## = 0.7219
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: cartera[, i]
## Dickey-Fuller Z(alpha) = -18.894, Truncation lag parameter = 7, p-value
## = 0.08835
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: cartera[, i]
## Dickey-Fuller Z(alpha) = -7.5302, Truncation lag parameter = 7, p-value
## = 0.6897
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: cartera[, i]
## Dickey-Fuller Z(alpha) = 4.1525, Truncation lag parameter = 7, p-value
## = 0.99
## alternative hypothesis: stationaryIBM: El p-value de la acción del IBM tiene un valor de 0.04129 lo cual es menor a 0.05, por lo que se rechaza la hipotesis nula. La serie es estacionaria.
BABA: El p-value de la acción de Alibaba tiene un valor de 0.3592 que es mayor a 0.05, por lo que no se rechaza la hipotisis nula. La serie presenta raiz unitaria.
AMZN: El p-value de la acción de Amazon tiene un valor de 0.7859 que es mayor a 0.05, por lo que no se rechaza la hipotisis nula. La serie presenta raiz unitaria.
FB: El p-value de la acción de Facebook tiene un valor de 0.09156 que es mayor a 0.05, por lo que no se rechaza la hipotisis nula. La serie presenta raiz unitaria.
MSFT: El p-value de la acción de Microsoft tiene un valor de 0.7067 que es mayor a 0.05, por lo que no se rechaza la hipotisis nula. La serie presenta raiz unitaria.
TSLA: El p-value de la acción de Tesla tiene un valor de 0.99 que es mayor a 0.05, por lo que no se rechaza la hipotisis nula. La serie presenta raiz unitaria.
Rendimiento
#=======================================================================
#Prueba de Prueba de Phillips-Perron
#=======================================================================
j=6
for (i in 1:j) {
print(pp.test(rendimiento[,i]))
}##
## Phillips-Perron Unit Root Test
##
## data: rendimiento[, i]
## Dickey-Fuller Z(alpha) = -1582.8, Truncation lag parameter = 7, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: rendimiento[, i]
## Dickey-Fuller Z(alpha) = -1308.4, Truncation lag parameter = 7, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: rendimiento[, i]
## Dickey-Fuller Z(alpha) = -1434.3, Truncation lag parameter = 7, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: rendimiento[, i]
## Dickey-Fuller Z(alpha) = -1473.5, Truncation lag parameter = 7, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: rendimiento[, i]
## Dickey-Fuller Z(alpha) = -1694.1, Truncation lag parameter = 7, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## Phillips-Perron Unit Root Test
##
## data: rendimiento[, i]
## Dickey-Fuller Z(alpha) = -1462.7, Truncation lag parameter = 7, p-value
## = 0.01
## alternative hypothesis: stationaryAl analizar todas las pruebas de raíz unitaria de los rendimientos de las acciones, tenemos como resultado un p-value menor al 5% por lo cual rechazamos la hipótesis nula. Todas las series presentan estacionariedad.
Modelo ARMA
\[ y_{t}=c+\Phi_{1}y_{t-1}+\Phi_{2}y_{t-2}+\cdots+\Phi_{p}y_{t-p}+\varepsilon_{t}+\theta_{1}\varepsilon_{t-1}+\theta_{2}\varepsilon_{t-2}+\cdots+\theta_{q}\varepsilon_{t-q} \]
O de la siguiente forma:
\[ \Phi(L)y_{t}=c+\theta(L)\varepsilon_{t} \]
Es estacionario si todas las raices de \(\Phi(L)\) caen fuera del circulo unitario.
Es invertible si todas la raices de \(\theta(L)\) caen fuera del circulo
ACF y PACF
Para determinar a nuestros procesos autorregresivos (p) utilizamos el comando pacf(). Para determinar a nuestras medias móviles (q) utilizamos el comando acf().
#===========================================================================================
# ACF y PACF
#===========================================================================================
attach(rendimiento)
autoplot(acf(R.IBM,plot = FALSE)) # q= 1-7
autoplot(pacf(R.IBM,plot = FALSE))# p= 1-7
#===========================================================================================
# MEJOR MODELO
#===========================================================================================
datos<-NULL
indice<- NULL
for(i in 1:7){
for(a in 1:7){
ata<- summary(arma(rendimiento$R.IBM,order = c(i,a)))$aic
datos<- c(datos,ata)
atita<- paste(i,a)
indice<- c(indice,atita)
table<- data.frame("ARMA"=indice,"AIC"=datos)
}
}head(ARMA , n=20)| ARMA | AIC |
|---|---|
| 1 1 | -7837087 |
| 1 2 | -7835607 |
| 1 3 | -7684702 |
| 1 4 | -7647744 |
| 1 5 | -7778381 |
| 1 6 | -7792616 |
| 1 7 | -7797409 |
| 2 1 | -7836622 |
| 2 2 | -7836861 |
| 2 3 | -7687635 |
| 2 4 | -7588449 |
| 2 5 | -7681415 |
| 2 6 | -7793536 |
| 2 7 | -7805270 |
| 3 1 | -7476097 |
| 3 2 | -7707118 |
| 3 3 | -7871656 |
| 3 4 | -7748682 |
| 3 5 | 1264748 |
| 3 6 | -7768506 |
El mejor modelo garch que podemos estimar es el ARMA(3,3), ya que presenta el menor valor AIC de todos los modelos que hemos estimado y eso nos induce a la maxima verosimilitud.
Modelo ARIMA
Una vez que detectamos que la serie es una marcha aleatoria (tiene una raíz unitaria), la serie requiere ser diferenciada. Si buscamos proyectar la serie en diferencias y empleamos un modelo ARMA, en realidad vamos a estimar un modelo ARIMA donde:
- AR= Preceso Autorregresivo
- I= Número de Integraciones
- MA= Precos de Medias Moviles
\[ \triangle Y_{t}=c+\Phi{}\triangle Y_{t-1}+\varepsilon_{t}+\theta_{2}\varepsilon_{t-1} \]
El paquete tseries permite utilizar el comando arima() Para crear nuestro modelo arima
#===========================================================================================
# MEJOR MODELO
#===========================================================================================
Modelarima=arima(cartera$IBM, order = c(3,1,3)) #ar=3, d=1 , q=3
summary(Modelarima)##
## Call:
## arima(x = cartera$IBM, order = c(3, 1, 3))
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3
## -0.7795 0.8437 0.8831 0.7257 -0.8896 -0.8362
## s.e. 0.0527 0.0161 0.0430 0.0683 0.0156 0.0603
##
## sigma^2 estimated as 3.536: log likelihood = -2939.56, aic = 5893.12
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.0142788 1.879722 1.274 -0.01022733 1.021042 1.002703 0.002215734Ruido Blanco
\[ Y_{t}=\varepsilon_{t}, \varepsilon_{t}\longrightarrow\text{N} (0,\sigma^{2}) \] Primer Momento \[ E(\text{Y}_{t})=0 \] Segundo Momento \[ \text{VAR}(\text{Y}_{t})=\sigma^{2} \]
\[ \text{COV}(\text{Y}_{t},\text{Y}_{t-k})=0 \]
#===========================================================================================
# PRUEBA DE RAÍZ UNITARIA EN LOS RESIDUOS
#===========================================================================================
residuos=residuos<- as.vector(na.omit(Modelarima$residuals))
Box.test(residuos)##
## Box-Pierce test
##
## data: residuos
## X-squared = 0.0070402, df = 1, p-value = 0.9331ggtsdiag(Modelarima)
Como presenciamos tanto en el gráfico como en la prueba de raíz unitaria los p-values de nuestros residuos son mayores al 5% por lo que no rechazamos la hipótesis de existencia de raíz unitaria.
Forecast
Forecasting es el proceso de hacer predicciones sobre el futuro mediante el análisis estadístico de tendencias observadas en datos históricos. Dicho de otra manera: utilizar el pasado para conocer el futuro. Para realizarlo utilizaremos el comando forecast()
#===========================================================================================
# PRONOSTICO
#===========================================================================================
pronostico=forecast(Modelarima, h=40)
head(pronostico)## $method
## [1] "ARIMA(3,1,3)"
##
## $model
##
## Call:
## arima(x = cartera$IBM, order = c(3, 1, 3))
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3
## -0.7795 0.8437 0.8831 0.7257 -0.8896 -0.8362
## s.e. 0.0527 0.0161 0.0430 0.0683 0.0156 0.0603
##
## sigma^2 estimated as 3.536: log likelihood = -2939.56, aic = 5893.12
##
## $level
## [1] 80 95
##
## $mean
## Time Series:
## Start = 1435
## End = 1474
## Frequency = 1
## [1] 121.9164 121.5376 122.1055 121.7463 122.1710 122.0385 122.1828 122.3335
## [9] 122.2208 122.5633 122.3343 122.7022 122.5247 122.7712 122.7543 122.8187
## [17] 122.9719 122.8919 123.1403 123.0145 123.2516 123.1800 123.3247 123.3609
## [25] 123.3915 123.5260 123.4790 123.6561 123.5971 123.7510 123.7377 123.8258
## [33] 123.8819 123.9008 124.0111 123.9906 124.1164 124.0985 124.2005 124.2169
##
## $lower
## Time Series:
## Start = 1435
## End = 1474
## Frequency = 1
## 80% 95%
## 1435 119.5058 118.2297
## 1436 118.2178 116.4604
## 1437 118.0813 115.9511
## 1438 117.1175 114.6672
## 1439 117.0641 114.3607
## 1440 116.4530 113.4962
## 1441 116.2218 113.0662
## 1442 115.9808 112.6178
## 1443 115.5460 112.0126
## 1444 115.5657 111.8614
## 1445 115.0467 111.1888
## 1446 115.1451 111.1446
## 1447 114.7025 110.5617
## 1448 114.7176 110.4543
## 1449 114.4605 110.0701
## 1450 114.3186 109.8190
## 1451 114.2579 109.6450
## 1452 113.9879 109.2744
## 1453 114.0478 109.2345
## 1454 113.7439 108.8363
## 1455 113.8143 108.8185
## 1456 113.5761 108.4921
## 1457 113.5708 108.4074
## 1458 113.4531 108.2083
## 1459 113.3456 108.0277
## 1460 113.3400 107.9478
## 1461 113.1634 107.7027
## 1462 113.2139 107.6861
## 1463 113.0325 107.4400
## 1464 113.0714 107.4180
## 1465 112.9431 107.2287
## 1466 112.9254 107.1551
## 1467 112.8744 107.0475
## 1468 112.7946 106.9153
## 1469 112.8064 106.8749
## 1470 112.6926 106.7117
## 1471 112.7279 106.6992
## 1472 112.6217 106.5463
## 1473 112.6403 106.5207
## 1474 112.5737 106.4101
##
## $upper
## Time Series:
## Start = 1435
## End = 1474
## Frequency = 1
## 80% 95%
## 1435 124.3269 125.6030
## 1436 124.8574 126.6148
## 1437 126.1297 128.2600
## 1438 126.3751 128.8255
## 1439 127.2778 129.9812
## 1440 127.6240 130.5808
## 1441 128.1438 131.2993
## 1442 128.6863 132.0492
## 1443 128.8955 132.4289
## 1444 129.5609 133.2652
## 1445 129.6219 133.4798
## 1446 130.2593 134.2598
## 1447 130.3469 134.4878
## 1448 130.8248 135.0881
## 1449 131.0480 135.4385
## 1450 131.3187 135.8184
## 1451 131.6858 136.2987
## 1452 131.7959 136.5094
## 1453 132.2329 137.0461
## 1454 132.2850 137.1926
## 1455 132.6888 137.6846
## 1456 132.7839 137.8678
## 1457 133.0785 138.2419
## 1458 133.2686 138.5135
## 1459 133.4373 138.7553
## 1460 133.7120 139.1041
## 1461 133.7945 139.2552
## 1462 134.0983 139.6261
## 1463 134.1617 139.7543
## 1464 134.4306 140.0840
## 1465 134.5324 140.2467
## 1466 134.7263 140.4966
## 1467 134.8893 140.7163
## 1468 135.0070 140.8863
## 1469 135.2159 141.1474
## 1470 135.2886 141.2695
## 1471 135.5049 141.5336
## 1472 135.5752 141.6506
## 1473 135.7606 141.8802
## 1474 135.8602 142.0237autoplot(pronostico, main="Pronostico de BABA de los futuros 40 días")
Paquete Var
VAR Modelo econométrico multivariado, de carácter autoregresivo, debido a que utiliza los rezagos de una de las variables y lo contrastan con los rezagos de las demás variables del modelo.
library(vars)## Loading required package: MASS## Loading required package: strucchange## Loading required package: sandwich## Loading required package: lmtestlibrary(forecast)
library(foreign)Importamos la base de datos
Vamos a trabajar con dos variables: Oferta monetaria identificada con la abreviación M2 e Inflación identificada con la abreviación INPC
library(readxl)
varinfla <- read_excel("C:/Users/ASUS/Downloads/varinfla.xlsx")
head(varinfla, n=20)| M2 | INPC |
|---|---|
| 28.7740 | 59.8083 |
| 29.3109 | 60.3388 |
| 29.8290 | 60.6734 |
| 30.1613 | 61.0186 |
| 30.4289 | 61.2467 |
| 30.9230 | 61.6095 |
| 31.6270 | 61.8498 |
| 31.7013 | 62.1896 |
| 32.0940 | 62.6439 |
| 32.0057 | 63.0753 |
| 32.4261 | 63.6146 |
| 32.6579 | 64.3033 |
| 32.6008 | 64.6598 |
| 33.5838 | 64.6170 |
| 34.0825 | 65.0264 |
| 34.4749 | 65.3544 |
| 34.6724 | 65.5044 |
| 35.0376 | 65.6593 |
| 35.4592 | 65.4887 |
| 36.4135 | 65.8767 |
Hay que convertir primeramente el archivo en una serie de tiempo (ts) que será mucho más útil de poder analizarla:
# Generar serie de tiempo para Oferta de Dinero (M2)
tm2=ts(varinfla[,1], start = c(2000,1), frequency = 12)
# Generar serie de tiempo para INPC
tp=ts(varinfla[,2], start = c(2000,1), frequency = 12)Primeramente, utilizamos logaritmos y posteriormente diferenciaciones para poder lograr estacionalidad en las variables:
# Generar logaritmos para las variables
# Para M2
ltm2<-log(tm2)
# Para INPC
ltp<-log(tp)Gráfica de las series
# Para graficar
par(mfrow=c(1,1))
ts.plot(ltp,ltm2,col=c("blue","red"))
Ncesitamos saber cuántas veces es necesaria que una variable sea diferenciada para lograr la estacionaridad Utilizamos número de diferenciaciones ndiffs()
ndiffs(ltm2)## [1] 2ndiffs(ltp)## [1] 1Procederemos a dercivar nuestras datos con el comando diff()
# Primera derivada de log de INPC
dltp<-diff(ltp)
# Segunda derivada de log de INPC
d2ltp=diff(dltp)
# Primera derivada de log de M2
dltm2<-diff(ltm2)
# Segunda derivada de log de M2
d2ltm2=diff(dltm2)Gráficas de las derivadas de las variables INPC y M2
# Graficando las derivadas de las variables INPC y M2
ts.plot(d2ltp, d2ltm2, col=c("blue", "red"))
Causalidad de granger
¿La consecuencia de la Oferta Monetaria tiene su origen en la Inflación o es la Inflación la consecuencia de la Oferta Monetaria?
Causalidad de M2 a INPC
Ho : La Oferta de Dinero (M2) no causa (afecta) a los Precios (INPC) > 0.05
H1 : La Oferta de Dinero (M2) si causa (afecta) a los Precios (INPC) < 0.05
Primer rezago
grangertest(d2ltp~d2ltm2, order=1)| Res.Df | Df | F | Pr(>F) |
|---|---|---|---|
| 170 | NA | NA | NA |
| 171 | -1 | 0.8795894 | 0.3496447 |
Primer rezago: Se acepta Ho, es decir M2 no afecta INPC (F Pr 0.3496)
Segundo rezago
grangertest(d2ltp~d2ltm2, order=2)| Res.Df | Df | F | Pr(>F) |
|---|---|---|---|
| 167 | NA | NA | NA |
| 169 | -2 | 0.421632 | 0.6566717 |
Segundo rezago: Se acepta Ho, es decir M2 no afecta INPC (F Pr 0.6567)
Tercer rezago
grangertest(d2ltp~d2ltm2, order=3)| Res.Df | Df | F | Pr(>F) |
|---|---|---|---|
| 164 | NA | NA | NA |
| 167 | -3 | 0.2980917 | 0.8267412 |
Tercer rezago: Se acepta Ho, es decir M2 no afecta INPC (F Pr 0.8267)
Cuarto rezago
grangertest(d2ltp~d2ltm2, order=4)| Res.Df | Df | F | Pr(>F) |
|---|---|---|---|
| 161 | NA | NA | NA |
| 165 | -4 | 2.710505 | 0.0320184 |
Cuarto rezago: Se rechaza Ho, es decir M2 si afecta INPC (F Pr 0.03202)
Causalidad de INPC a M2
Ho : Los Precios (INPC) no causa (afecta) a la Oferta de Dinero (M2) > 0.05 H1 : Los Precios (INPC) no causa (afecta) a la Oferta de Dinero (M2) < 0.05
Primer rezago
grangertest(d2ltm2~d2ltp, order=1)| Res.Df | Df | F | Pr(>F) |
|---|---|---|---|
| 170 | NA | NA | NA |
| 171 | -1 | 0.0908867 | 0.7634213 |
Primer rezago: Se acepta Ho, es decir INPC no afecta M2 (F Pr 0.7634)
Décimo rezago
grangertest(d2ltm2~d2ltp, order=10)| Res.Df | Df | F | Pr(>F) |
|---|---|---|---|
| 143 | NA | NA | NA |
| 153 | -10 | 1.760201 | 0.0731166 |
Décimo rezago: Se acepta Ho, es decir INPC no afecta M2 (F Pr 0.07312)
Esto quiere decir que nunca se acepta que INPC afecte a la M2
Crear nuevo objeto para VAR con las variables estacionarias
vard2ltm2=ts(d2ltm2, start=2000, frequency=10)
vard2ltp=ts(d2ltp, start=2000, frequency=10)
ejvar=cbind(vard2ltm2, vard2ltp)
print(ejvar)## Time Series:
## Start = c(2000, 1)
## End = c(2017, 4)
## Frequency = 10
## vard2ltm2 vard2ltp
## 2000.0 -0.0009656447 -3.300864e-03
## 2000.1 -0.0064430432 1.433194e-04
## 2000.2 -0.0022454019 -1.942120e-03
## 2000.3 0.0072742598 2.174874e-03
## 2000.4 0.0064035137 -2.013323e-03
## 2000.5 -0.0201644392 1.586132e-03
## 2000.6 0.0099649039 1.799609e-03
## 2000.7 -0.0150664921 -4.155866e-04
## 2000.8 0.0158047270 1.650813e-03
## 2000.9 -0.0059265096 2.254195e-03
## 2001.0 -0.0088730913 -5.239221e-03
## 2001.1 0.0314569386 -6.190872e-03
## 2001.2 -0.0149667317 6.977952e-03
## 2001.3 -0.0032927813 -1.284381e-03
## 2001.4 -0.0057350086 -2.738878e-03
## 2001.5 0.0047653308 6.938669e-05
## 2001.6 0.0014831800 -4.963577e-03
## 2001.7 0.0145958761 8.508847e-03
## 2001.8 -0.0142772414 3.359543e-03
## 2001.9 -0.0020401552 -4.757453e-03
## 2002.0 0.0102406429 -7.493690e-04
## 2002.1 -0.0119120420 -2.376678e-03
## 2002.2 -0.0168888485 7.805078e-03
## 2002.3 0.0217069284 -9.830555e-03
## 2002.4 0.0050543500 5.743571e-03
## 2002.5 -0.0108292217 3.468257e-04
## 2002.6 -0.0010265422 -3.423306e-03
## 2002.7 0.0065279437 2.838752e-03
## 2002.8 -0.0041124272 -1.996990e-03
## 2002.9 -0.0083273029 9.279053e-04
## 2003.0 0.0035996601 2.203648e-03
## 2003.1 0.0024811310 -1.601151e-03
## 2003.2 0.0045389594 3.658899e-03
## 2003.3 0.0096318710 -3.713197e-03
## 2003.4 -0.0159336405 -3.078636e-04
## 2003.5 0.0076303038 -1.261123e-03
## 2003.6 -0.0018470875 3.518818e-03
## 2003.7 -0.0125354435 -4.587421e-03
## 2003.8 0.0205292106 -4.937218e-03
## 2003.9 -0.0123601637 4.059175e-03
## 2004.0 0.0082810134 6.207614e-04
## 2004.1 -0.0147877468 1.546898e-03
## 2004.2 0.0099141118 2.940433e-03
## 2004.3 -0.0004298882 -2.275070e-03
## 2004.4 0.0095211657 4.606121e-03
## 2004.5 0.0078812381 -3.976974e-03
## 2004.6 -0.0345416385 1.906965e-03
## 2004.7 0.0092926219 -2.322832e-04
## 2004.8 0.0232625468 -2.580838e-03
## 2004.9 -0.0233207029 -1.875028e-03
## 2005.0 0.0030061446 -4.020139e-03
## 2005.1 0.0119419398 4.113677e-03
## 2005.2 -0.0154335193 1.015504e-03
## 2005.3 0.0001925633 3.537022e-03
## 2005.4 0.0116919246 2.080755e-03
## 2005.5 -0.0003235563 -1.333408e-03
## 2005.6 -0.0039087062 1.592438e-03
## 2005.7 0.0150296349 -6.430308e-03
## 2005.8 -0.0169129832 -2.027544e-03
## 2005.9 0.0008938633 3.290152e-03
## 2006.0 0.0140946961 1.170862e-03
## 2006.1 -0.0212348273 -9.419461e-04
## 2006.2 0.0151762071 -6.070256e-03
## 2006.3 0.0005392421 1.554334e-03
## 2006.4 -0.0104422142 4.867123e-03
## 2006.5 0.0031031862 -2.712739e-03
## 2006.6 0.0025801935 2.805645e-03
## 2006.7 0.0043022503 -1.547461e-03
## 2006.8 -0.0020854570 4.719695e-03
## 2006.9 -0.0065375363 -1.048068e-03
## 2007.0 0.0021215328 -2.764838e-04
## 2007.1 0.0047121568 -4.318427e-03
## 2007.2 -0.0021305229 -2.742516e-04
## 2007.3 -0.0070880590 2.107601e-04
## 2007.4 -0.0133381185 -5.926028e-03
## 2007.5 0.0254550678 5.323591e-03
## 2007.6 -0.0144913343 1.876376e-03
## 2007.7 -0.0040488707 2.350334e-03
## 2007.8 0.0138230404 4.955049e-03
## 2007.9 -0.0077958419 -5.681694e-03
## 2008.0 0.0170086392 8.709111e-04
## 2008.1 0.0095222854 5.337172e-04
## 2008.2 -0.0324840149 -6.158620e-04
## 2008.3 0.0094367374 -2.359720e-03
## 2008.4 -0.0006788772 -6.303641e-04
## 2008.5 -0.0131973740 -2.758192e-03
## 2008.6 0.0216596393 -4.293509e-03
## 2008.7 -0.0067165994 6.090790e-03
## 2008.8 0.0010056133 3.037773e-03
## 2008.9 0.0003685911 -1.726515e-04
## 2009.0 -0.0032425089 3.669315e-03
## 2009.1 -0.0039171221 -3.845367e-03
## 2009.2 0.0138264544 3.140722e-03
## 2009.3 -0.0038356531 -2.904514e-03
## 2009.4 -0.0048027366 4.981865e-04
## 2009.5 -0.0034446193 -1.655513e-03
## 2009.6 0.0041665137 4.253795e-03
## 2009.7 -0.0043215314 -4.948926e-03
## 2009.8 0.0037637710 -3.354650e-03
## 2009.9 -0.0138527844 5.211072e-03
## 2010.0 0.0125473452 1.428201e-03
## 2010.1 -0.0030381451 1.998493e-04
## 2010.2 0.0124337100 1.034705e-03
## 2010.3 -0.0008792738 -1.663343e-06
## 2010.4 0.0062059713 4.512291e-03
## 2010.5 0.0346517958 -4.401623e-03
## 2010.6 -0.0474924494 -4.586251e-03
## 2010.7 -0.0160262067 -1.100275e-04
## 2010.8 0.0143375679 3.530679e-03
## 2010.9 -0.0022555799 -2.241614e-03
## 2011.0 -0.0046845933 -6.411269e-03
## 2011.1 0.0009379857 4.756749e-03
## 2011.2 0.0072088651 8.809519e-04
## 2011.3 -0.0094252829 -3.310929e-04
## 2011.4 0.0072476740 2.614121e-03
## 2011.5 0.0056404973 -1.982801e-03
## 2011.6 -0.0048856272 2.153140e-03
## 2011.7 -0.0005313973 -1.043522e-03
## 2011.8 -0.0089354641 6.680997e-03
## 2011.9 0.0066777336 -5.044067e-03
## 2012.0 0.0057734358 1.305947e-03
## 2012.1 -0.0126999675 -1.026479e-02
## 2012.2 0.0159985950 -3.129268e-03
## 2012.3 -0.0040113168 6.007953e-03
## 2012.4 0.0071575871 2.481411e-03
## 2012.5 -0.0082967966 6.046531e-04
## 2012.6 0.0003263858 2.455062e-03
## 2012.7 -0.0084801335 9.259169e-04
## 2012.8 -0.0009986335 1.826049e-03
## 2012.9 0.0080032082 -3.038436e-03
## 2013.0 -0.0026087628 -8.216876e-05
## 2013.1 0.0011224692 -1.115309e-03
## 2013.2 0.0010306492 -1.827853e-03
## 2013.3 -0.0010353560 -1.995946e-03
## 2013.4 -0.0005180177 -7.319772e-03
## 2013.5 0.0037881254 7.349164e-03
## 2013.6 0.0032352507 4.836537e-03
## 2013.7 0.0034178950 -3.206050e-03
## 2013.8 0.0060473346 8.698036e-04
## 2013.9 -0.0157200082 4.274476e-03
## 2014.0 0.0026226442 4.033213e-03
## 2014.1 0.0014988951 -2.574031e-03
## 2014.2 -0.0013007220 -1.130269e-03
## 2014.3 -0.0039180629 -5.022855e-03
## 2014.4 0.0041655904 -1.456827e-03
## 2014.5 -0.0050358383 -3.716026e-03
## 2014.6 0.0108550818 -1.952801e-05
## 2014.7 -0.0042922230 7.761186e-03
## 2014.8 0.0010784426 9.988571e-04
## 2014.9 -0.0093059519 -2.601974e-03
## 2015.0 -0.0018778205 1.401118e-03
## 2015.1 0.0063698251 6.490278e-04
## 2015.2 0.0069633209 1.723851e-03
## 2015.3 -0.0165391660 -4.474105e-03
## 2015.4 0.0063414395 1.723604e-03
## 2015.5 0.0014308158 8.899776e-04
## 2015.6 -0.0006560887 2.400921e-03
## 2015.7 -0.0017996569 -6.650610e-03
## 2015.8 0.0030126978 -3.993886e-03
## 2015.9 -0.0015516428 2.726267e-03
## 2016.0 0.0049329896 2.758893e-04
## 2016.1 0.0017991528 3.172438e-03
## 2016.2 0.0006590120 9.162040e-04
## 2016.3 0.0007355575 9.878215e-04
## 2016.4 0.0013661606 4.533737e-03
## 2016.5 -0.0146513136 -3.558836e-03
## 2016.6 0.0120330086 3.181373e-03
## 2016.7 -0.0031824817 -6.371310e-03
## 2016.8 0.0004630717 2.058411e-04
## 2016.9 0.0052105665 -4.603223e-03
## 2017.0 -0.0058410488 -1.335619e-03
## 2017.1 -0.0038726265 4.934402e-03
## 2017.2 0.0056098149 1.014936e-03
## 2017.3 -0.0006490686 8.391137e-04Proceso VAR
VARselect(ejvar, lag.max = 10)## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 10 8 2 10
##
## $criteria
## 1 2 3 4 5
## AIC(n) -2.039908e+01 -2.062690e+01 -2.060197e+01 -2.070022e+01 -2.068785e+01
## HQ(n) -2.035304e+01 -2.055017e+01 -2.049454e+01 -2.056210e+01 -2.051904e+01
## SC(n) -2.028567e+01 -2.043788e+01 -2.033735e+01 -2.035999e+01 -2.027201e+01
## FPE(n) 1.382917e-09 1.101202e-09 1.129076e-09 1.023541e-09 1.036468e-09
## 6 7 8 9 10
## AIC(n) -2.085454e+01 -2.093593e+01 -2.101046e+01 -2.100572e+01 -2.105399e+01
## HQ(n) -2.065504e+01 -2.070573e+01 -2.074957e+01 -2.071414e+01 -2.073171e+01
## SC(n) -2.036310e+01 -2.036888e+01 -2.036780e+01 -2.028746e+01 -2.026012e+01
## FPE(n) 8.775590e-10 8.092568e-10 7.514889e-10 7.555070e-10 7.204384e-10VARselect(ejvar, lag.max = 12)## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 11 11 2 11
##
## $criteria
## 1 2 3 4 5
## AIC(n) -2.046463e+01 -2.068196e+01 -2.065764e+01 -2.075149e+01 -2.075348e+01
## HQ(n) -2.041820e+01 -2.060458e+01 -2.054931e+01 -2.061220e+01 -2.058323e+01
## SC(n) -2.035027e+01 -2.049137e+01 -2.039081e+01 -2.040842e+01 -2.033417e+01
## FPE(n) 1.295173e-09 1.042211e-09 1.067940e-09 9.723977e-10 9.706467e-10
## 6 7 8 9 10
## AIC(n) -2.090388e+01 -2.097478e+01 -2.104458e+01 -2.103653e+01 -2.109132e+01
## HQ(n) -2.070268e+01 -2.074263e+01 -2.078147e+01 -2.074247e+01 -2.076631e+01
## SC(n) -2.040834e+01 -2.040300e+01 -2.039656e+01 -2.031228e+01 -2.029083e+01
## FPE(n) 8.353390e-10 7.784502e-10 7.263246e-10 7.326459e-10 6.941160e-10
## 11 12
## AIC(n) -2.130916e+01 -2.130390e+01
## HQ(n) -2.095320e+01 -2.091699e+01
## SC(n) -2.043244e+01 -2.035094e+01
## FPE(n) 5.587598e-10 5.623294e-10Se maneja el modelo hasta con 12 rezagos preferible a 10 debido a que 3 de los componentes indican que debe haber hasta 11 variables de rezago.
Var 1
Generamos un nuevo modelo var1 que permita mostrar los coeficientes que se refieren a la oferta de dinero. A continuación, realizamos algunas pruebas de especificación del modelo var con summary por lo que revisamos el resultado de las raíces de características polinomiales y para saber que se satisface la condición de estabilidad deberán de ser menores a uno (< 1)
var1<-VAR(ejvar, p=11)
summary(var1)##
## VAR Estimation Results:
## =========================
## Endogenous variables: vard2ltm2, vard2ltp
## Deterministic variables: const
## Sample size: 163
## Log Likelihood: 1316.416
## Roots of the characteristic polynomial:
## 0.9851 0.9851 0.9604 0.9604 0.9425 0.9425 0.9343 0.9343 0.906 0.906 0.8852 0.8852 0.8749 0.8749 0.8717 0.8717 0.8679 0.8553 0.8553 0.8127 0.8127 0.7702
## Call:
## VAR(y = ejvar, p = 11)
##
##
## Estimation results for equation vard2ltm2:
## ==========================================
## vard2ltm2 = vard2ltm2.l1 + vard2ltp.l1 + vard2ltm2.l2 + vard2ltp.l2 + vard2ltm2.l3 + vard2ltp.l3 + vard2ltm2.l4 + vard2ltp.l4 + vard2ltm2.l5 + vard2ltp.l5 + vard2ltm2.l6 + vard2ltp.l6 + vard2ltm2.l7 + vard2ltp.l7 + vard2ltm2.l8 + vard2ltp.l8 + vard2ltm2.l9 + vard2ltp.l9 + vard2ltm2.l10 + vard2ltp.l10 + vard2ltm2.l11 + vard2ltp.l11 + const
##
## Estimate Std. Error t value Pr(>|t|)
## vard2ltm2.l1 -7.630e-01 8.274e-02 -9.221 4.04e-16 ***
## vard2ltp.l1 -1.714e-01 2.356e-01 -0.728 0.468104
## vard2ltm2.l2 -8.434e-01 1.012e-01 -8.333 6.58e-14 ***
## vard2ltp.l2 1.110e-01 2.530e-01 0.438 0.661704
## vard2ltm2.l3 -6.063e-01 1.216e-01 -4.988 1.78e-06 ***
## vard2ltp.l3 -6.402e-03 2.703e-01 -0.024 0.981138
## vard2ltm2.l4 -6.979e-01 1.257e-01 -5.550 1.38e-07 ***
## vard2ltp.l4 -6.657e-02 2.754e-01 -0.242 0.809320
## vard2ltm2.l5 -6.034e-01 1.338e-01 -4.509 1.37e-05 ***
## vard2ltp.l5 -1.468e-01 2.772e-01 -0.529 0.597328
## vard2ltm2.l6 -5.912e-01 1.314e-01 -4.498 1.43e-05 ***
## vard2ltp.l6 1.071e-01 2.444e-01 0.438 0.661785
## vard2ltm2.l7 -4.821e-01 1.316e-01 -3.664 0.000351 ***
## vard2ltp.l7 -5.209e-01 2.800e-01 -1.860 0.064914 .
## vard2ltm2.l8 -4.042e-01 1.261e-01 -3.206 0.001667 **
## vard2ltp.l8 5.844e-02 2.781e-01 0.210 0.833898
## vard2ltm2.l9 -2.958e-01 1.205e-01 -2.455 0.015307 *
## vard2ltp.l9 -2.264e-01 2.731e-01 -0.829 0.408476
## vard2ltm2.l10 -2.607e-01 1.010e-01 -2.580 0.010896 *
## vard2ltp.l10 -3.519e-01 2.542e-01 -1.385 0.168380
## vard2ltm2.l11 -1.952e-01 8.057e-02 -2.423 0.016665 *
## vard2ltp.l11 -4.569e-02 2.370e-01 -0.193 0.847435
## const -1.773e-05 6.388e-04 -0.028 0.977897
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.008133 on 140 degrees of freedom
## Multiple R-Squared: 0.5428, Adjusted R-squared: 0.4709
## F-statistic: 7.555 on 22 and 140 DF, p-value: 6.685e-15
##
##
## Estimation results for equation vard2ltp:
## =========================================
## vard2ltp = vard2ltm2.l1 + vard2ltp.l1 + vard2ltm2.l2 + vard2ltp.l2 + vard2ltm2.l3 + vard2ltp.l3 + vard2ltm2.l4 + vard2ltp.l4 + vard2ltm2.l5 + vard2ltp.l5 + vard2ltm2.l6 + vard2ltp.l6 + vard2ltm2.l7 + vard2ltp.l7 + vard2ltm2.l8 + vard2ltp.l8 + vard2ltm2.l9 + vard2ltp.l9 + vard2ltm2.l10 + vard2ltp.l10 + vard2ltm2.l11 + vard2ltp.l11 + const
##
## Estimate Std. Error t value Pr(>|t|)
## vard2ltm2.l1 -0.0153917 0.0265236 -0.580 0.5626
## vard2ltp.l1 -0.5768877 0.0755409 -7.637 3.16e-12 ***
## vard2ltm2.l2 0.0225320 0.0324482 0.694 0.4886
## vard2ltp.l2 -0.6496240 0.0811166 -8.009 4.05e-13 ***
## vard2ltm2.l3 0.0258940 0.0389673 0.665 0.5075
## vard2ltp.l3 -0.6720339 0.0866516 -7.756 1.65e-12 ***
## vard2ltm2.l4 0.0795081 0.0403071 1.973 0.0505 .
## vard2ltp.l4 -0.6540235 0.0882744 -7.409 1.09e-11 ***
## vard2ltm2.l5 0.0019056 0.0429004 0.044 0.9646
## vard2ltp.l5 -0.5936082 0.0888574 -6.680 5.19e-10 ***
## vard2ltm2.l6 0.0257631 0.0421322 0.611 0.5419
## vard2ltp.l6 -0.7731698 0.0783469 -9.869 < 2e-16 ***
## vard2ltm2.l7 -0.0057926 0.0421757 -0.137 0.8910
## vard2ltp.l7 -0.6635451 0.0897558 -7.393 1.19e-11 ***
## vard2ltm2.l8 -0.0051973 0.0404152 -0.129 0.8979
## vard2ltp.l8 -0.6685684 0.0891632 -7.498 6.74e-12 ***
## vard2ltm2.l9 0.0220922 0.0386188 0.572 0.5682
## vard2ltp.l9 -0.5278806 0.0875485 -6.030 1.39e-08 ***
## vard2ltm2.l10 0.0046915 0.0323905 0.145 0.8850
## vard2ltp.l10 -0.4810434 0.0814811 -5.904 2.56e-08 ***
## vard2ltm2.l11 0.0081196 0.0258292 0.314 0.7537
## vard2ltp.l11 -0.4276816 0.0759902 -5.628 9.59e-08 ***
## const -0.0001443 0.0002048 -0.704 0.4823
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.002607 on 140 degrees of freedom
## Multiple R-Squared: 0.5602, Adjusted R-squared: 0.4911
## F-statistic: 8.107 on 22 and 140 DF, p-value: 5.963e-16
##
##
##
## Covariance matrix of residuals:
## vard2ltm2 vard2ltp
## vard2ltm2 6.615e-05 7.967e-07
## vard2ltp 7.967e-07 6.798e-06
##
## Correlation matrix of residuals:
## vard2ltm2 vard2ltp
## vard2ltm2 1.00000 0.03757
## vard2ltp 0.03757 1.00000Todas las raices de caracter polinomila son inferiores a la unidad por lo que el modelo está balanceado en y es de orden 11.
predict(var1)## $vard2ltm2
## fcst lower upper CI
## [1,] 0.0026504351 -0.01329049 0.01859136 0.01594093
## [2,] -0.0012903644 -0.02138019 0.01879946 0.02008982
## [3,] 0.0004468823 -0.02012240 0.02101617 0.02056929
## [4,] 0.0002362415 -0.02065101 0.02112349 0.02088725
## [5,] -0.0021789296 -0.02329058 0.01893272 0.02111165
## [6,] 0.0014087991 -0.01970894 0.02252654 0.02111774
## [7,] -0.0015125259 -0.02270137 0.01967632 0.02118885
## [8,] -0.0007353639 -0.02217193 0.02070120 0.02143656
## [9,] -0.0001379709 -0.02184007 0.02156413 0.02170210
## [10,] -0.0007812784 -0.02249881 0.02093625 0.02171753
##
## $vard2ltp
## fcst lower upper CI
## [1,] -0.0005427679 -0.005652973 0.004567437 0.005110205
## [2,] 0.0024101137 -0.003499161 0.008319388 0.005909275
## [3,] 0.0021511447 -0.004004144 0.008306434 0.006155289
## [4,] -0.0020013764 -0.008190028 0.004187275 0.006188651
## [5,] 0.0002112159 -0.006001921 0.006424353 0.006213137
## [6,] -0.0036325779 -0.010031449 0.002766293 0.006398871
## [7,] -0.0005470646 -0.007009053 0.005914924 0.006461988
## [8,] -0.0019499228 -0.008423373 0.004523528 0.006473451
## [9,] -0.0012872773 -0.007770857 0.005196302 0.006483579
## [10,] 0.0026061353 -0.003968118 0.009180389 0.006574254layout(1:2)Gráfico de Var1
plot(var1)
