1 Cargando librerías

library(tidyverse)
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## v readr   1.4.0     v forcats 0.5.1
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library(lubridate)
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library(car)
## Loading required package: carData
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library(tseries)
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library(astsa)
library(foreign)
library(timsac)
library(vars)
## Loading required package: MASS
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## Loading required package: strucchange
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library(lmtest)
library(mFilter)
library(dynlm)
library(nlme)
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library(lmtest)
library(broom)
library(kableExtra)
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library(knitr)
library(MASS)
library(parallel)
library(car)
library(mlogit)
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library(dplyr)
library(tidyr)

library(forecast)
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#install.packages('fpp2', dependencies = TRUE)
library(fpp2)
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#Note que los modelos SARIMA especificados como ARIMA(p, d, q)(P, D, Q) m son modelos ARIMA con un gran numero de restricciones.
#donde (P, D, Q)m denota la parte estacional del modelo.

2 Importando la base de datos.

#Procedimiento general

#Importar los datos de la libreria fpp2
data(euretail)
euretail
##        Qtr1   Qtr2   Qtr3   Qtr4
## 1996  89.13  89.52  89.88  90.12
## 1997  89.19  89.78  90.03  90.38
## 1998  90.27  90.77  91.85  92.51
## 1999  92.21  92.52  93.62  94.15
## 2000  94.69  95.34  96.04  96.30
## 2001  94.83  95.14  95.86  95.83
## 2002  95.73  96.36  96.89  97.01
## 2003  96.66  97.76  97.83  97.76
## 2004  98.17  98.55  99.31  99.44
## 2005  99.43  99.84 100.32 100.40
## 2006  99.88 100.19 100.75 101.01
## 2007 100.84 101.34 101.94 102.10
## 2008 101.56 101.48 101.13 100.34
## 2009  98.93  98.31  97.67  97.44
## 2010  96.53  96.56  96.51  96.70
## 2011  95.88  95.84  95.79  95.94

3 Determinando el número de diferenciaciones estacionales.

#Comando para saber cuantas diferenciaciones se requieren para un SARIMA
nsdiffs(euretail)
## [1] 1
#Comando para saber cuantas diferenciaciones se requieren para un SARIMA
ndiffs(euretail)
## [1] 2

4 Realizar la gráfica de la serie de tiempo.

#Realiza la grafica de serie de tiempo
plot.ts(euretail, main="Euretail")

# Correlograma de Función de Autocorrelación Simple.

acf(euretail)

# Correlograma de Función de Autocorrelación Simple.

pacf(euretail)

5 Solicitar el mejor modelo de ARIMA

#Solicitar el mejor modelo de ARIMA
#La funcion auto.arima() calcula el mejor modelo ARIMA(p, d, q) de acuerdo a diferentes criterios: AIC, AICC o BIC value.
model=auto.arima(euretail,stepwise=FALSE,approximation=FALSE)

6 Resumen del Modelo SARIMA

#Resumen del Modelo SARIMA
summary(model)
## Series: euretail 
## ARIMA(0,1,3)(0,1,1)[4] 
## 
## Coefficients:
##          ma1     ma2     ma3     sma1
##       0.2630  0.3694  0.4200  -0.6636
## s.e.  0.1237  0.1255  0.1294   0.1545
## 
## sigma^2 estimated as 0.156:  log likelihood=-28.63
## AIC=67.26   AICc=68.39   BIC=77.65
## 
## Training set error measures:
##                       ME      RMSE       MAE         MPE      MAPE      MASE
## Training set -0.02965298 0.3661147 0.2787802 -0.02795377 0.2885545 0.2267735
##                     ACF1
## Training set 0.006455781

7 Residuales del modelo.

residuals=resid(model)
plot(residuals, main="Residuals", col="Blue")

adf.test(residuals)
## 
##  Augmented Dickey-Fuller Test
## 
## data:  residuals
## Dickey-Fuller = -3.8579, Lag order = 3, p-value = 0.02164
## alternative hypothesis: stationary

8 Pronóstico del modelo.

#SARIMA(0,1,3)(0,1,1)[4] 

#Pronóstico del modelo
forecast(model,h=10)
##         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## 2012 Q1       95.17620 94.67006 95.68233 94.40214 95.95026
## 2012 Q2       95.23809 94.42273 96.05345 93.99111 96.48507
## 2012 Q3       95.32444 94.16364 96.48523 93.54915 97.09972
## 2012 Q4       95.33633 93.77859 96.89408 92.95397 97.71870
## 2013 Q1       94.56087 92.58895 96.53279 91.54508 97.57666
## 2013 Q2       94.57178 92.23497 96.90859 90.99794 98.14562
## 2013 Q3       94.56911 91.88684 97.25138 90.46694 98.67129
## 2013 Q4       94.58101 91.56075 97.60126 89.96193 99.20009
## 2014 Q1       93.80554 90.40685 97.20423 88.60769 99.00339
## 2014 Q2       93.81646 90.05855 97.57436 88.06923 99.56368
ggseasonplot(euretail, main="Plot SARIMA")