# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# INGENIERIA ESTADISTICA E INFORMATICA
# CURSO: SERIES DE TIEMPO
library(readxl)
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library(lubridate)
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## date, intersect, setdiff, union
library(tidyverse)
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library(car)
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library(tseries)
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library(astsa)
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library(foreign)
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library(timsac)
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library(vars)
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library(lmtest)
library(mFilter)
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library(dynlm)
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library(nlme)
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## collapse
library(broom)
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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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library(fpp2)
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library(stats)
library(quantmod)
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## first, last
## Loading required package: TTR
#Modelo SARIMA
#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
#Realice la grafica de Serie de Tiempo
plot.ts(euretail, main = "Euretail",type ="l")
adf.test(euretail) #No Estacionaria
## Warning in adf.test(euretail): p-value greater than printed p-value
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## Augmented Dickey-Fuller Test
##
## data: euretail
## Dickey-Fuller = -0.17892, Lag order = 3, p-value = 0.99
## alternative hypothesis: stationary
#Diferencias se requieren para un SARIMA
nsdiffs(euretail)
## [1] 1
acf(euretail)
pacf(euretail)
#Solicitar Modelo de ARIMA
model <- auto.arima(euretail, stepwise = F, approximation = F)
# 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
residuals <- resid(model)
plot(residuals, main = "Residuals", col = "Blue")
adf.test(residuals)
##
## Augmented Dickey-Fuller Test
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## data: residuals
## Dickey-Fuller = -3.8579, Lag order = 3, p-value = 0.02164
## alternative hypothesis: stationary
#SARIMA(0,1,3),(0,1,1)[4]
#Pronsotico 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 = "SARIMA")
#Otra forma para hacer ARIMA
modelo2 <- Arima(euretail, order = c(0,1,3), seasonal = list(order=c(0,1,1), period(4)))
summary(modelo2)
## 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