ANALISIS ARIMA DE LA PRODUCCION MANUFACTURERA
Paquetes
library(TSA)##
## Attaching package: 'TSA'## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarlibrary(ggfortify)## Loading required package: ggplot2library(forecast)
library(fpp)## Loading required package: fma## Loading required package: expsmooth## Loading required package: lmtest## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: tserieslibrary(seasonal)
library(fpp2)##
## Attaching package: 'fpp2'## The following objects are masked from 'package:fpp':
##
## ausair, ausbeer, austa, austourists, debitcards, departures,
## elecequip, euretail, guinearice, oil, sunspotarea, usmeleclibrary(gridExtra)
library(urca)
library(foreign)
library(vars)## Loading required package: MASS##
## Attaching package: 'MASS'## The following objects are masked from 'package:fma':
##
## cement, housing, petrol## Loading required package: strucchange## Loading required package: sandwichlibrary(zoo)
library(dynlm)
library(lmtest)
library(strucchange)
library(readxl)
library(seasonalview)##
## Attaching package: 'seasonalview'## The following object is masked from 'package:seasonal':
##
## view1. Breve descripcion de la serie elegida, asi como su frecuencia, unidad de medida, fuente, etc.
Serie: PM
2006-2018, incluye serie original, desestacionalizada.
Unidad de medida:indice.
Periodicidad: Mensual
Fuente:(www.inegi.org.mx)
2. Graficar los datos, analizar patrones y observaciones atipicas. Apoye su analisis con una descomposicion clasica.
base<-read_xls("C:/Users/rodar/OneDrive/Escritorio/SERIES/INDUSTRIA MANUFACTURERA.xls")
PM<-ts(base$PM, frequency = 12, start=c(2006,1))
autoplot(PM) + xlab("Year")+ylab("INDICE") +
ggtitle('INDUSTRIA MANUFACTURERA (PM ORIGINAL)')
fit <- decompose(PM,type = "additive")
autoplot(fit)
3. Si es necesario, utilizar transformacion Box-Cox/logaritmos para estabilizar la varianza.
PMlog <-log(PM)
plot(PMlog)
Se utilizo la aplicacion de un logaritmo ya que se hiba a estabilizar la varianza para visualizar el comportamiento de la serie.
4. En caso de estacionalidad, aplicar diferencias estacionales.
PMdif <-diff(PMlog)
plot(PMlog)
PMdif2 <-diff(log(PM))BoxCox.ar(PM)## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
## Warning in arima0(x, order = c(i, 0L, 0L), include.mean = demean): possible
## convergence problem: optim gave code = 1
plot(PMdif2) 
Sabemos que contiene un valor =0 muy cerca de su centro por lo que sugiere este una transformacion logaritmica.
plot(PM^1.5, type="o")
plot(diff(PM^1.5), type="o")
plot(diff(PMdif2))
Se agrearon dos diferencias.
5. Usar preba Dickey-Fuller para evaluar el orden de integracion de la serie. Diferenciar hasta que la serie sea estacionaria.
summary(ur.df(PM))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.6093 -1.1080 -0.2844 2.0807 4.9716
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 0.003696 0.003588 1.030 0.308
## z.diff.lag 0.115448 0.138306 0.835 0.408
##
## Residual standard error: 2.675 on 49 degrees of freedom
## Multiple R-squared: 0.04397, Adjusted R-squared: 0.004953
## F-statistic: 1.127 on 2 and 49 DF, p-value: 0.3323
##
##
## Value of test-statistic is: 1.03
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.6 -1.95 -1.61No es estacionaria debido a que el valor de P es de 0.3323, y no es apto para 0.5
summary(ur.df(PMdif2))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.088854 -0.008099 0.000222 0.022948 0.052844
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.84361 0.18071 -4.668 2.47e-05 ***
## z.diff.lag 0.04486 0.13834 0.324 0.747
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02737 on 48 degrees of freedom
## Multiple R-squared: 0.405, Adjusted R-squared: 0.3802
## F-statistic: 16.33 on 2 and 48 DF, p-value: 3.884e-06
##
##
## Value of test-statistic is: -4.6684
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.6 -1.95 -1.61Como podemos ver ya es estacionaria.
6. Usar herramientas ACF, PACF, EACF y criterios de Akaike/ Bayes para construir propuestas de modelos.
ggAcf(PMdif2)
ggPacf(PMdif2) 
eacf(PMdif2)## AR/MA
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0 o o o o o o o o o o o o o o
## 1 x o o o o o o o o o o o o o
## 2 x x o o o o o o o o o o o o
## 3 x o x o o o o o o o o o o o
## 4 x o x o o o o o o o o o o o
## 5 o o o o o o o o o o o o o o
## 6 x o o x o o o o o o o o o o
## 7 x o o x o o o o o o o o o oggtsdisplay(PMdif2)
PM2 <-armasubsets(y=PMdif2,nar= 12, nma=12, y.name="test", ar.method="ols")## Warning in leaps.setup(x, y, wt = wt, nbest = nbest, nvmax = nvmax,
## force.in = force.in, : 2 linear dependencies foundplot(PM2)
propuesta1<- Arima(PMdif2, order = c(1,0,0),method = "ML")
propuesta1## Series: PMdif2
## ARIMA(1,0,0) with non-zero mean
##
## Coefficients:
## ar1 mean
## 0.1540 0.0056
## s.e. 0.1402 0.0044
##
## sigma^2 estimated as 0.0007603: log likelihood=113.95
## AIC=-221.9 AICc=-221.4 BIC=-216.04propuesta2 <-Arima(PMdif2, order = c(0,0,2),method = "ML")
propuesta2## Series: PMdif2
## ARIMA(0,0,2) with non-zero mean
##
## Coefficients:
## ma1 ma2 mean
## 0.1863 0.0439 0.0057
## s.e. 0.1784 0.1484 0.0046
##
## sigma^2 estimated as 0.0007736: log likelihood=114.02
## AIC=-220.03 AICc=-219.18 BIC=-212.237. Como parte del diagnostico del modelo, analizar los residuos y aplicar la prueba Ljung-Box.
tsdiag(propuesta1,gof=12, omit.initial=F)
tsdiag(propuesta2,gof=12, omit.initial=F)
Como podemos ver. en las dos se ajustan los residuos, ya que los valores son arriba de P.
8. Usar la funcion auto.arima () y compare sus resultados con el inciso anterior.
propuesta.auto<-auto.arima(PMdif2)
propuesta.auto## Series: PMdif2
## ARIMA(0,0,0) with zero mean
##
## sigma^2 estimated as 0.0007783: log likelihood=112.33
## AIC=-222.67 AICc=-222.59 BIC=-220.72checkresiduals(propuesta.auto)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,0,0) with zero mean
## Q* = 11.041, df = 10.4, p-value = 0.3883
##
## Model df: 0. Total lags used: 10.4propuesta2 <- auto.arima(PMdif2, stepwise = FALSE, approximation = FALSE)
propuesta2## Series: PMdif2
## ARIMA(1,0,2) with zero mean
##
## Coefficients:
## ar1 ma1 ma2
## -0.8872 1.2367 0.4829
## s.e. 0.3140 0.1993 0.2908
##
## sigma^2 estimated as 0.0006855: log likelihood=116.81
## AIC=-225.62 AICc=-224.77 BIC=-217.82checkresiduals(propuesta2)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,0,2) with zero mean
## Q* = 9.4314, df = 7.4, p-value = 0.2556
##
## Model df: 3. Total lags used: 10.4Se puede observar que en las dos propuestas,la media ya es estable asi como los residuales.
9. Presente la ecuacion final y describa.
\[ Yt= -0.8872e_1+1.2367e_{t-1}+0.4829e_{t-2}+et \]
10. Crear un pronostico a dos años.
pronostico<- plot(forecast(propuesta.auto, h=24))
pronostico## $mean
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2010 0 0 0 0 0 0 0
## 2011 0 0 0 0 0 0 0 0 0 0 0 0
## 2012 0 0 0 0 0
##
## $lower
## 80% 95%
## Jun 2010 -0.03575187 -0.05467777
## Jul 2010 -0.03575187 -0.05467777
## Aug 2010 -0.03575187 -0.05467777
## Sep 2010 -0.03575187 -0.05467777
## Oct 2010 -0.03575187 -0.05467777
## Nov 2010 -0.03575187 -0.05467777
## Dec 2010 -0.03575187 -0.05467777
## Jan 2011 -0.03575187 -0.05467777
## Feb 2011 -0.03575187 -0.05467777
## Mar 2011 -0.03575187 -0.05467777
## Apr 2011 -0.03575187 -0.05467777
## May 2011 -0.03575187 -0.05467777
## Jun 2011 -0.03575187 -0.05467777
## Jul 2011 -0.03575187 -0.05467777
## Aug 2011 -0.03575187 -0.05467777
## Sep 2011 -0.03575187 -0.05467777
## Oct 2011 -0.03575187 -0.05467777
## Nov 2011 -0.03575187 -0.05467777
## Dec 2011 -0.03575187 -0.05467777
## Jan 2012 -0.03575187 -0.05467777
## Feb 2012 -0.03575187 -0.05467777
## Mar 2012 -0.03575187 -0.05467777
## Apr 2012 -0.03575187 -0.05467777
## May 2012 -0.03575187 -0.05467777
##
## $upper
## 80% 95%
## Jun 2010 0.03575187 0.05467777
## Jul 2010 0.03575187 0.05467777
## Aug 2010 0.03575187 0.05467777
## Sep 2010 0.03575187 0.05467777
## Oct 2010 0.03575187 0.05467777
## Nov 2010 0.03575187 0.05467777
## Dec 2010 0.03575187 0.05467777
## Jan 2011 0.03575187 0.05467777
## Feb 2011 0.03575187 0.05467777
## Mar 2011 0.03575187 0.05467777
## Apr 2011 0.03575187 0.05467777
## May 2011 0.03575187 0.05467777
## Jun 2011 0.03575187 0.05467777
## Jul 2011 0.03575187 0.05467777
## Aug 2011 0.03575187 0.05467777
## Sep 2011 0.03575187 0.05467777
## Oct 2011 0.03575187 0.05467777
## Nov 2011 0.03575187 0.05467777
## Dec 2011 0.03575187 0.05467777
## Jan 2012 0.03575187 0.05467777
## Feb 2012 0.03575187 0.05467777
## Mar 2012 0.03575187 0.05467777
## Apr 2012 0.03575187 0.05467777
## May 2012 0.03575187 0.0546777712. Utilizando metodos de pronosticos y/o suavizamiento exponencial generar un pronostico para dos años. Elegir el metodo que presenta la raiz del error medio al cuadrado mas pequeño.
PMRSME<-window(PM, start=2006)
autoplot(PMRSME)+
ylab("PM(indice)")+xlab("Año")
Se aplica un suavizamiento exponencial simple, debido a que los datos no tienen una clara estacionalidad.
PMRSME<-window(PM,start=2006)
PMFC<-ses(PMRSME, h=5)
round(accuracy(PMFC),2)## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.57 2.73 1.91 0.5 1.87 0.21 0.11El pronostico se hace como:
autoplot(PMFC)+
autolayer(fitted(PMFC),series="Fitted")+
ylab("PM(indice)")+xlab("Año")
13. Analizar un VAR, necesita incluir los puntos siguientes:
Se procedera a limpiar la consola
rm(list = ls())base2<-read_xls("C:/Users/rodar/OneDrive/Escritorio/SERIES/V Y P.xls")Declaramos ambas variables como series de tiempo.
ts.V <- ts(base2$VOL, start = c(2006,1), frequency = 12)
ts.P <- ts(base2$PROD, start = c(2006,1), frequency = 12)autoplot(ts.V)
autoplot(ts.P)
ggseasonplot(ts.V)
ggseasonplot(ts.P)
mes. <- season(ts.V)
reg.w <- lm(ts.V ~ time(ts.V) + mes.)
summary(reg.w)##
## Call:
## lm(formula = ts.V ~ time(ts.V) + mes.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.30 -1.86 1.17 2.64 8.38
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.319e+04 1.204e+03 -10.956 1.30e-13 ***
## time(ts.V) 6.620e+00 5.995e-01 11.043 1.02e-13 ***
## mes.February 2.788e+00 3.496e+00 0.798 0.430
## mes.March 1.317e+00 3.497e+00 0.377 0.709
## mes.April 1.650e-01 3.499e+00 0.047 0.963
## mes.May -1.567e+00 3.501e+00 -0.447 0.657
## mes.June -7.783e-01 3.708e+00 -0.210 0.835
## mes.July -7.800e-01 3.707e+00 -0.210 0.834
## mes.August -5.567e-01 3.708e+00 -0.150 0.881
## mes.September -1.633e+00 3.709e+00 -0.440 0.662
## mes.October 1.890e+00 3.710e+00 0.509 0.613
## mes.November 7.133e-01 3.713e+00 0.192 0.849
## mes.December -5.883e-01 3.716e+00 -0.158 0.875
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.527 on 40 degrees of freedom
## Multiple R-squared: 0.7597, Adjusted R-squared: 0.6876
## F-statistic: 10.54 on 12 and 40 DF, p-value: 5.981e-09mes. <- season(ts.P)
reg.p <- lm(ts.P ~ time(ts.P) + mes.)
summary(reg.p)##
## Call:
## lm(formula = ts.P ~ time(ts.P) + mes.)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.2071 -1.6494 0.3165 1.8506 7.3600
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.786e+03 6.939e+02 -8.338 2.77e-10 ***
## time(ts.P) 2.933e+00 3.456e-01 8.487 1.75e-10 ***
## mes.February 2.236e+00 2.015e+00 1.109 0.274
## mes.March 8.312e-01 2.016e+00 0.412 0.682
## mes.April 1.068e-01 2.017e+00 0.053 0.958
## mes.May -9.977e-01 2.018e+00 -0.494 0.624
## mes.June 1.034e+00 2.137e+00 0.484 0.631
## mes.July 9.900e-01 2.137e+00 0.463 0.646
## mes.August 1.071e+00 2.137e+00 0.501 0.619
## mes.September 6.512e-01 2.138e+00 0.305 0.762
## mes.October 3.132e+00 2.139e+00 1.464 0.151
## mes.November 1.462e+00 2.140e+00 0.683 0.498
## mes.December -3.206e-02 2.142e+00 -0.015 0.988
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.186 on 40 degrees of freedom
## Multiple R-squared: 0.6604, Adjusted R-squared: 0.5585
## F-statistic: 6.481 on 12 and 40 DF, p-value: 3.159e-06Aplicamos las transformaciones necesarios (ej. diferencias y log)
ts.ddV <- diff(diff(ts.V,12)) # diferencia de volumen
ts.dP <- diff(diff(ts.P,12)) # diferencia de produccionggtsdisplay(ts.ddV)
ggtsdisplay(ts.dP)
summary(ur.df(ts.ddV))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.4919 -1.5118 0.2825 1.4929 10.3051
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.6803 0.1677 -4.057 0.000255 ***
## z.diff.lag 0.2339 0.1606 1.456 0.154059
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.473 on 36 degrees of freedom
## Multiple R-squared: 0.3214, Adjusted R-squared: 0.2837
## F-statistic: 8.524 on 2 and 36 DF, p-value: 0.0009318
##
##
## Value of test-statistic is: -4.0571
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61summary(ur.df(ts.dP))##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.3684 -1.5291 -0.3147 1.0707 8.2205
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.9422 0.2013 -4.680 3.98e-05 ***
## z.diff.lag 0.2143 0.1618 1.325 0.194
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.902 on 36 degrees of freedom
## Multiple R-squared: 0.4195, Adjusted R-squared: 0.3872
## F-statistic: 13.01 on 2 and 36 DF, p-value: 5.604e-05
##
##
## Value of test-statistic is: -4.6797
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.62 -1.95 -1.61Se deben guardar ambas variables en un único objeto.
base3 <- cbind.zoo(v = ts.ddV, p = ts.dP) # ocupamos función 'zoo' del paquete del mismo nombre.
View(base3) # la serie está cortada por las diferencias
autoplot(base3) # la serie está cortada por las diferencias
Las variables tienen la misma longitud, por lo tanto no restringimos la muestra.
Ocupamos ‘base3’ para comenzar nuestro análisis VAR.
VARselect(base3, lag.max = 24, type = "const")[["selection"]]## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 8 8VARselect(base3, lag.max = 24, type = "const")## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 8 8
##
## $criteria
## 1 2 3 4 5
## AIC(n) -0.1854425 -0.12242399 -0.031133019 -0.09513740 -0.1647990
## HQ(n) -0.1706065 -0.09769719 0.003484502 -0.05062916 -0.1104001
## SC(n) 0.1042782 0.36044396 0.644882113 0.77402491 0.8975104
## FPE(n) 0.8382296 0.92388316 1.100105692 1.22237287 1.5809072
## 6 7 8 9 10 11 12 13 14 15
## AIC(n) -0.5163828 -3.738693e+01 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## HQ(n) -0.4520931 -3.731275e+01 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## SC(n) 0.7390739 -3.593833e+01 -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## FPE(n) 2.1618932 1.309731e-15 0 0 0 0 0 0 0 0
## 16 17 18 19 20 21 22 23 24
## AIC(n) -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## HQ(n) -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## SC(n) -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf -Inf
## FPE(n) 0 0 0 0 0 0 0 0 0var1 <- VAR(base3, p=1, type = "both")
summary(var1)##
## VAR Estimation Results:
## =========================
## Endogenous variables: v, p
## Deterministic variables: both
## Sample size: 39
## Log Likelihood: -144.32
## Roots of the characteristic polynomial:
## 0.5143 0.5143
## Call:
## VAR(y = base3, p = 1, type = "both")
##
##
## Estimation results for equation v:
## ==================================
## v = v.l1 + p.l1 + const + trend
##
## Estimate Std. Error t value Pr(>|t|)
## v.l1 0.24932 0.32966 0.756 0.455
## p.l1 0.30426 0.43750 0.695 0.491
## const -0.20905 1.24810 -0.167 0.868
## trend 0.01299 0.05333 0.244 0.809
##
##
## Residual standard error: 3.627 on 35 degrees of freedom
## Multiple R-Squared: 0.2178, Adjusted R-squared: 0.1507
## F-statistic: 3.248 on 3 and 35 DF, p-value: 0.03333
##
##
## Estimation results for equation p:
## ==================================
## p = v.l1 + p.l1 + const + trend
##
## Estimate Std. Error t value Pr(>|t|)
## v.l1 -0.3512278 0.2684137 -1.309 0.1992
## p.l1 0.6320899 0.3562198 1.774 0.0847 .
## const -0.0734402 1.0162147 -0.072 0.9428
## trend -0.0008388 0.0434190 -0.019 0.9847
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 2.953 on 35 degrees of freedom
## Multiple R-Squared: 0.09608, Adjusted R-squared: 0.0186
## F-statistic: 1.24 on 3 and 35 DF, p-value: 0.3099
##
##
##
## Covariance matrix of residuals:
## v p
## v 13.16 10.381
## p 10.38 8.721
##
## Correlation matrix of residuals:
## v p
## v 1.0000 0.9691
## p 0.9691 1.0000causality(var1, cause='v')$Granger##
## Granger causality H0: v do not Granger-cause p
##
## data: VAR object var1
## F-Test = 1.7123, df1 = 1, df2 = 70, p-value = 0.195causality(var1, cause='p')$Granger##
## Granger causality H0: p do not Granger-cause v
##
## data: VAR object var1
## F-Test = 0.48365, df1 = 1, df2 = 70, p-value = 0.4891plot(irf(var1, impulse='v', response = 'p'))
plot(irf(var1, impulse='p', response = 'v'))
var.serial <- serial.test(var1, lags.pt = 12)var.serial##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object var1
## Chi-squared = 74.069, df = 44, p-value = 0.00305plot(var.serial)
Otra propuesta
VARselect(base3, lag.max = 24, type = "const")[["selection"]]## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 8 8var8 <- VAR(base3, p=8, type = "both")
summary(var8)##
## VAR Estimation Results:
## =========================
## Endogenous variables: v, p
## Deterministic variables: both
## Sample size: 32
## Log Likelihood: -66.074
## Roots of the characteristic polynomial:
## 0.9639 0.9639 0.9366 0.9366 0.9313 0.9313 0.9183 0.9183 0.8899 0.8776 0.8776 0.8104 0.8104 0.6932 0.6932 0.3462
## Call:
## VAR(y = base3, p = 8, type = "both")
##
##
## Estimation results for equation v:
## ==================================
## v = v.l1 + p.l1 + v.l2 + p.l2 + v.l3 + p.l3 + v.l4 + p.l4 + v.l5 + p.l5 + v.l6 + p.l6 + v.l7 + p.l7 + v.l8 + p.l8 + const + trend
##
## Estimate Std. Error t value Pr(>|t|)
## v.l1 2.1739 1.2546 1.733 0.1051
## p.l1 -2.2419 1.5620 -1.435 0.1732
## v.l2 0.0728 1.1495 0.063 0.9504
## p.l2 -0.5155 1.5173 -0.340 0.7391
## v.l3 -1.2295 0.8997 -1.367 0.1933
## p.l3 0.7749 1.1681 0.663 0.5179
## v.l4 -1.3367 0.9013 -1.483 0.1602
## p.l4 1.7021 1.2289 1.385 0.1877
## v.l5 1.0267 0.9039 1.136 0.2751
## p.l5 -0.9041 1.0070 -0.898 0.3845
## v.l6 0.8322 0.9789 0.850 0.4096
## p.l6 -1.4776 1.0598 -1.394 0.1850
## v.l7 0.9043 0.8158 1.109 0.2863
## p.l7 -1.2288 0.9255 -1.328 0.2055
## v.l8 -1.6594 0.7197 -2.306 0.0369 *
## p.l8 1.5987 0.5985 2.671 0.0183 *
## const 2.3102 1.8040 1.281 0.2211
## trend -0.1056 0.0801 -1.319 0.2084
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 2.53 on 14 degrees of freedom
## Multiple R-Squared: 0.7429, Adjusted R-squared: 0.4306
## F-statistic: 2.379 on 17 and 14 DF, p-value: 0.0539
##
##
## Estimation results for equation p:
## ==================================
## p = v.l1 + p.l1 + v.l2 + p.l2 + v.l3 + p.l3 + v.l4 + p.l4 + v.l5 + p.l5 + v.l6 + p.l6 + v.l7 + p.l7 + v.l8 + p.l8 + const + trend
##
## Estimate Std. Error t value Pr(>|t|)
## v.l1 1.74893 1.04814 1.669 0.1174
## p.l1 -2.04967 1.30503 -1.571 0.1386
## v.l2 0.03780 0.96039 0.039 0.9692
## p.l2 -0.58133 1.26764 -0.459 0.6536
## v.l3 -0.69914 0.75167 -0.930 0.3681
## p.l3 0.17918 0.97589 0.184 0.8570
## v.l4 -1.41934 0.75304 -1.885 0.0804 .
## p.l4 1.46959 1.02672 1.431 0.1743
## v.l5 1.12675 0.75519 1.492 0.1579
## p.l5 -1.11323 0.84132 -1.323 0.2070
## v.l6 0.61823 0.81787 0.756 0.4622
## p.l6 -1.16930 0.88543 -1.321 0.2078
## v.l7 0.49830 0.68154 0.731 0.4768
## p.l7 -0.82255 0.77324 -1.064 0.3054
## v.l8 -1.28531 0.60127 -2.138 0.0507 .
## p.l8 1.26514 0.50004 2.530 0.0240 *
## const 1.41944 1.50714 0.942 0.3623
## trend -0.09381 0.06692 -1.402 0.1828
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 2.113 on 14 degrees of freedom
## Multiple R-Squared: 0.7282, Adjusted R-squared: 0.3981
## F-statistic: 2.206 on 17 and 14 DF, p-value: 0.07054
##
##
##
## Covariance matrix of residuals:
## v p
## v 6.398 5.241
## p 5.241 4.466
##
## Correlation matrix of residuals:
## v p
## v 1.0000 0.9803
## p 0.9803 1.0000causality(var8, cause='v')$Granger##
## Granger causality H0: v do not Granger-cause p
##
## data: VAR object var8
## F-Test = 2.8017, df1 = 8, df2 = 28, p-value = 0.02052causality(var8, cause='p')$Granger##
## Granger causality H0: p do not Granger-cause v
##
## data: VAR object var8
## F-Test = 2.6585, df1 = 8, df2 = 28, p-value = 0.02628plot(irf(var8, impulse='v', response = 'p'))
plot(irf(var8, impulse='p', response = 'v'))
var.serial <- serial.test(var8, lags.pt = 8)
var.serial##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object var8
## Chi-squared = 34.921, df = 0, p-value < 2.2e-16plot(var.serial)
14. Evaluar la potencial cointegracion usando la metodologia de Engle-Granger y Johan-Sen
rm(list = ls())
base4<-read_xls("C:/Users/rodar/OneDrive/Escritorio/SERIES/V Y P.xls")