library(tseries)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
library(forecast)
url="https://raw.githubusercontent.com/vmoprojs/DataLectures/master/pib_ec_const.csv"
datos=read.delim(url,sep=";")
demanda_interna=datos$DI/1000000
dit=ts(demanda_interna,start = c(2000,1),frequency = 4)

plot(dit,main = "Demanda Interna",xlab = "año",ylab = "")

La gráfica muestra la evolución de la DEMANDA INTERNA a lo largo deltiempo, desde el año 2000 hasta el finales del 2020, se observa una tendencia creciente

ditl=log(dit)
plot(ditl)

adf.test(ditl)
## Warning in adf.test(ditl): p-value greater than printed p-value
## 
##  Augmented Dickey-Fuller Test
## 
## data:  ditl
## Dickey-Fuller = -0.17559, Lag order = 4, p-value = 0.99
## alternative hypothesis: stationary

p-valor es 0.99, mayor que alfa entonces se acepta la hipotesis

m=auto.arima(ditl,trace = T)
## 
##  ARIMA(2,2,2)(1,0,1)[4]                    : -357.3024
##  ARIMA(0,2,0)                              : -321.8768
##  ARIMA(1,2,0)(1,0,0)[4]                    : -341.9503
##  ARIMA(0,2,1)(0,0,1)[4]                    : -362.7824
##  ARIMA(0,2,1)                              : -363.1886
##  ARIMA(0,2,1)(1,0,0)[4]                    : -363.3354
##  ARIMA(0,2,1)(2,0,0)[4]                    : -362.0084
##  ARIMA(0,2,1)(1,0,1)[4]                    : -362.3233
##  ARIMA(0,2,1)(2,0,1)[4]                    : -360.0544
##  ARIMA(0,2,0)(1,0,0)[4]                    : -328.0866
##  ARIMA(1,2,1)(1,0,0)[4]                    : -362.6642
##  ARIMA(0,2,2)(1,0,0)[4]                    : -362.5324
##  ARIMA(1,2,2)(1,0,0)[4]                    : -360.3985
## 
##  Best model: ARIMA(0,2,1)(1,0,0)[4]
m
## Series: ditl 
## ARIMA(0,2,1)(1,0,0)[4] 
## 
## Coefficients:
##           ma1    sar1
##       -0.9359  0.2145
## s.e.   0.0417  0.1409
## 
## sigma^2 = 0.0006463:  log likelihood = 184.82
## AIC=-363.64   AICc=-363.34   BIC=-356.42

\((y_t-y_{t-1})-(y_{t-12}-y_{t-13})=-0.9359\sigma_{t-1}+0.2145\sigma_{t-12}+E_t\)

dip=predict(m,19)
dip
## $pred
##          Qtr1     Qtr2     Qtr3     Qtr4
## 2021 2.788893 2.756976 2.757648 2.759689
## 2022 2.755888 2.745745 2.742592 2.739733
## 2023 2.735620 2.730148 2.726175 2.722264
## 2024 2.718085 2.713614 2.709465 2.705329
## 2025 2.701136 2.696880 2.692693         
## 
## $se
##            Qtr1       Qtr2       Qtr3       Qtr4
## 2021 0.02542271 0.03712318 0.04691225 0.05585256
## 2022 0.06721426 0.07789681 0.08819189 0.09826127
## 2023 0.10869913 0.11904141 0.12934367 0.13964497
## 2024 0.15006531 0.16053106 0.17105891 0.18166168
## 2025 0.19236692 0.20316444 0.21406036